## NCERT Exercise 3.3 Solution class six

In this section the question number 1 of NCERT Exercise 3.3 class six math has been solved. This question is related to divisibility test. In this question ten numbers have been given and test for divisibility by 2, 3, 4, 5, 6, 8, 9, 10 and 11 has been performed.

Question (1) Using divisibility tests, determine which of the following numbers are divisible by 2; by 3; by 4; by 5; by 6; by 8; by 9; by 10; by 11 (say, yes or no)

**Answer Table**

**Answer and Explanation**

**Answer** (ii) 990

**Is 990 divisible by 2: Yes**

**Explanation:**

Since 990 is an even number, thus it is divisible by 2.

990 ÷ 2 = 495

**Is 990 divisible by 3: Yes**

**Explanation:**

The sum of digits of 990 = 9 + 9 + 0 = 18.

Since the sum of the digits of 990 which is equal to 18 is divisible by 3, thus 990 is divisible by 3.

990 ÷ 3 = 330

**Is 990 divisible by 4: No**

**Explanation**

The last two digits of 990 is equal to 90, and 90 is not divisible by 4, thus 990 is not divisible by 4.

**Is 990 divisible by 5: Yes**

**Explanation**

The last digit of 990 is zero (0), thus 990 is divisible by 5.

990 ÷ 5 = 198

**Is 990 divisible by 6: Yes**

**Explanation**

Since, 990 is divisible by 2 and 3 both, thus 990 is divisible by 6.

990 ÷ 6 = 165

**Is 990 divisible by 8: No**

**Explanation**

Since, last three digits of 990 is not divisible by 8, thus 990 is not divisible by 8.

**Is 990 divisible by 9: Yes**

**Explanation**

Since the sum of digits of 990 which is equal to 18 is divisible by 9, thus 990 is divisible by 9.

990 ÷ 9 = 110

**Is 990 divisible by 10: Yes**

**Explanation**

Since, the last digit of 990 is zero (0), thus 990 is divisible by 10.

990 ÷ 10 = 99

**Is 990 divisible by 11: Yes**

**Explanation**

Since, the difference between the sum of digits at odd place and even place counting from right is equal to zero (0), thus 990 is divisible by 11

990 ÷ 11 = 90

**Answer** (iii) 1586

**Is 1586 divisible by 2: Yes**

**Explanation:**

Since 1586 is an even number, thus it is divisible by 2.

1586 ÷ 2 = 793

**Is 1586 divisible by 3: No**

**Explanation:**

The sum of digits of 1586 = 1 + 5 + 8 + 6 = 20.

Since the sum of the digits of 1586 which is equal to 20 is not divisible by 3, thus 1586 is not divisible by 3.

**Is 1586 divisible by 4: no**

**Explanation**

The last two digits of 1586 is equal to 86, and 86 is not divisible by 4, thus 1586 is not divisible by 4.

**Is 1586 divisible by 5: No**

**Explanation**

The last digit of 1586 is not zero (0) or five (5), thus 1586 is not divisible by 5.

**Is 1586 divisible by 6: No**

**Explanation**

Since, 1586 is divisible by 2 and not divisible by 3, thus 1586 is not divisible by 6.

**Is 1586 divisible by 8: No**

**Explanation**

Since, the last three digits of 1586 which is equal to 586 is not divisible by 8, thus 1586 is not divisible by 8.

**Is 1586 divisible by 9: No**

**Explanation**

The sum of digits of 1586 = 1 + 5 + 8 + 6 = 20.

Since the sum of the digits of 1586 which is equal to 20 is not divisible by 9, thus 1586 is not divisible by 9.

**Is 1586 divisible by 10: No**

**Explanation**

The last digit of 1586 is not zero (0), thus 1586 is not divisible by 10.

**Is 1586 divisible by 11: No**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 1586 is

= 6 + 5 – (8 + 1)

= 11 – 9 = 2

Since, the difference between the sum of digits at odd place and even place counting from right of 1586 is not equal to zero (0) or 11, thus 1586 is not divisible by 11

**Answer** (iv) 275

**Is 275 divisible by 2: No**

**Explanation:**

Since 275 is no an even number, thus it is not divisible by 2.

**Is 275 divisible by 3: No**

**Explanation:**

The sum of digits of 275 = 2 + 7 + 5 = 14.

Since the sum of the digits of 275 which is equal to 14 is not divisible by 3, thus Not is not divisible by 3.

**Is 275 divisible by 4: No**

**Explanation**

The last two digits of 275 is equal to 75, and 75 is not divisible by 4, thus 275 is not divisible by 4.

**Is 275 divisible by 5: Yes**

**Explanation**

The last digit of 275 is five (5), thus 275 is divisible by 5.

275 ÷ 5 = 55

**Is 275 divisible by 6: No**

**Explanation**

Since, 275 is neither divisible by 2 nor by 3, thus 275 is not divisible by 6.

**Is 275 divisible by 8: No**

**Explanation**

275 is is not divisible by 8.

**Is 275 divisible by 9: No**

**Explanation**

The sum of digits of 275 = 2 + 7 + 5 = 14.

Since the sum of the digits of 275 which is equal to 14 is not divisible by 9, thus 275 is not divisible by 9.

**Is 275 divisible by 10: No**

**Explanation**

The last digit of 275 is not zero (0), thus 275 is not divisible by 10.

**Is 275 divisible by 11: Yes**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 275 is

= 2 + 5 – (0 + 7)

= 7 – 7 = 0

Since, the difference between the sum of digits at odd place and even place counting from right of 275 is equal to zero (0), thus 275 is divisible by 11

275 ÷ 11 = 25

**Answer** (v) 6686

**Is 6686 divisible by 2: Yes**

**Explanation:**

Since 6686 is an even number, thus it is divisible by 2.

6686 ÷ 2 = 3343

**Is 6686 divisible by 3: No**

**Explanation:**

The sum of digits of 6686 = 6 + 6 + 8 + 6 = 26.

Since the sum of the digits of 6686 which is equal to 26 is not divisible by 3, thus 6686 is not divisible by 3.

**Is 6686 divisible by 4: No**

**Explanation**

The last two digits of 6686 is equal to 86, and 86 is not divisible by 4, thus 6686 is not divisible by 4.

**Is 6686 divisible by 5: No**

**Explanation**

The last digit of 6686 is not either five (5) or zero (0), thus 6686 is not divisible by 5.

**Is 6686 divisible by 6: No**

**Explanation**

Since, 6686 is divisible by 2 but not divisible by 3, thus 6686 is not divisible by 6.

**Is 6686 divisible by 8: No**

**Explanation**

The last three digits of 6686 counting from right is equal to 686 is not divisible by 8, thus 6686 is not divisible by 8.

**Is 6686 divisible by 9: No**

**Explanation**

The sum of digits of 6686 = 6 + 6 + 8 + 6 = 26.

Since the sum of the digits of 6686 which is equal to 26 is not divisible by 9, thus 6686 is not divisible by 9.

**Is 6686 divisible by 10: No**

**Explanation**

The last digit of 6686 is not zero (0), thus 6686 is not divisible by 10.

**Is 6686 divisible by 11: yes**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 275 is

= 8 + 6 – (6 + 6)

= 14 – 12 = 2

Since, the difference between the sum of digits of 6686 at odd place and even place counting from right is neither equal to zero (0) nor equal to 11, thus 6686 is not divisible by 11

**Answer** (vi) 639210

**Is 639210 divisible by 2: Yes**

**Explanation:**

Since 639210 is an even number, thus it is divisible by 2.

639210 ÷ 2 = 319605

**Is 639210 divisible by 3: Yes**

**Explanation:**

The sum of digits of 639210 = 6 + 3 + 9 + 2 + 1 + 0 = 21

Since the sum of the digits of 639210 which is equal to 21 is divisible by 3, thus 639210 is divisible by 3.

639210 ÷ 3 = 213070

**Is 639210 divisible by 4: No**

**Explanation**

The last two digits of 639210 is equal to 10, and 10 is not divisible by 4, thus 639210 is not divisible by 4.

**Is 639210 divisible by 5: Yes**

**Explanation**

The last digit of 639210 is zero (0), thus 639210 is divisible by 5.

639210 ÷ 5 = 63921

**Is 639210 divisible by 6: Yes**

**Explanation**

Since, 639210 is divisible by 2 and 3 both, thus 639210 is divisible by 6.

639210 ÷ 6 = 127842

**Is 639210 divisible by 8: No**

**Explanation**

The last three digits of 639210 counting from right is equal to 210 is not divisible by 8, thus 639210 is not divisible by 8.

**Is 639210 divisible by 9: No**

**Explanation**

The sum of digits of 639210 = 6 + 3 + 9 + 2 + 1 + 0 = 21

Since the sum of the digits of 639210 which is equal to 21 is not divisible by 9, thus 639210 is not divisible by 9.

**Is 639210 divisible by 10: Yes**

**Explanation**

The last digit of 639210 is zero (0), thus 639210 is divisible by 10.

639210 ÷ 10 = 63921

**Is 639210 divisible by 11: yes**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 639210 is

= 1 + 9 + 6 – (0 + 2 + 3)

= 16 – 5 = 11

Since, the difference between the sum of digits at odd place and even place counting from right of 639210 is equal to 11, thus 639210 is divisible by 11

639210 ÷ 11 = 58110

**Answer** (vii) 429714

**Is 429714 divisible by 2: Yes**

**Explanation:**

Since 429714 is an even number, thus it is divisible by 2.

429714 ÷ 2 = 214857

**Is 429714 divisible by 3: Yes**

**Explanation:**

The sum of digits of 429714 = 4 + 2 + 9 + 7 + 1 + 4 = 27

Since the sum of the digits of 429714 which is equal to 27 is divisible by 3, thus 429714 is divisible by 3.

429714 ÷ 3 = 143238

**Is 429714 divisible by 4: No**

**Explanation**

The last two digits of 429714 is equal to 14, and 14 is not divisible by 4, thus 429714 is not divisible by 4.

**Is 429714 divisible by 5: No**

**Explanation**

The last digit of 429714 is neither zero (0) nor five (5), thus 429714 is not divisible by 5.

**Is 429714 divisible by 6: Yes**

**Explanation**

Since, 429714 is divisible by 2 and 3 both, thus 429714 is divisible by 6.

429714 ÷ 6 = 71619

**Is 429714 divisible by 8: No**

**Explanation**

The last three digits of 429714 counting from right is equal to 714 is not divisible by 8, thus 429714 is not divisible by 8.

**Is 429714 divisible by 9: No**

**Explanation**

The sum of digits of 429714 = 4 + 2 + 9 + 7 + 1 + 4 = 27

Since the sum of the digits of 429714 which is equal to 27 is not divisible by 9, thus 429714 is not divisible by 9.

**Is 429714 divisible by 10: No**

**Explanation**

The last digit of 429714 is not zero (0), thus 429714 is not divisible by 10.

**Is 429714 divisible by 11: No**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 429714 is

= 1 + 9 + 4 – (4 + 7 + 2)

= 14 – 13 = 1

Since, the difference between the sum of digits at odd place and even place counting from right of 429714 is neither equal to zero not equal to 11, thus 429714 is not divisible by 11

**Answer** (viii) 2856

**Is 2856 divisible by 2: Yes**

**Explanation:**

Since 2856 is an even number, thus it is divisible by 2.

2856 ÷ 2 = 1428

**Is 2856 divisible by 3: Yes**

**Explanation:**

The sum of digits of 2856 = 2 + 8 + 5 + 6 = 21

Since the sum of the digits of 2856 which is equal to 21 is divisible by 3, thus 2856 is divisible by 3.

2856 ÷ 3 = 952

**Is 2856 divisible by 4: Yes**

**Explanation**

The last two digits of 2856 is equal to 56, and 56 is divisible by 4, thus 2856 is divisible by 4.

2856 ÷ 4 = 714

**Is 2856 divisible by 5: No**

**Explanation**

The last digit of 2856 is neither zero (0) nor five (5), thus 2856 is not divisible by 5.

**Is 2856 divisible by 6: Yes**

**Explanation**

Since, 2856 is divisible by 2 and 3 both, thus 2856 is divisible by 6.

2856 ÷ 6 = 476

**Is 2856 divisible by 8: Yes**

**Explanation**

The last three digits of 2856 counting from right is equal to 856 is divisible by 8, thus 2856 is divisible by 8.

2856 ÷ 8 = 357

**Is 2856 divisible by 9: No**

**Explanation**

The sum of digits of 2856 = 2 + 8 + 5 + 6 = 21

Since the sum of the digits of 2856 which is equal to 21 is not divisible by 9, thus 2856 is not divisible by 9.

**Is 2856 divisible by 10: No**

**Explanation**

The last digit of 2856 is not zero (0), thus 2856 is not divisible by 10.

**Is 2856 divisible by 11: No**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 2856 is

= 6 + 8 – (5 + 2)

= 14 – 7 = 7

Since, the difference between the sum of digits at odd place and even place counting from right of 2856 is neither equal to zero not equal to 11, thus 2856 is not divisible by 11

**Answer** (ix) 3060

**Is 3060 divisible by 2: Yes**

**Explanation:**

Since 3060 is an even number, thus it is divisible by 2.

3060 ÷ 2 = 1530

**Is 3060 divisible by 3: Yes**

**Explanation:**

The sum of digits of 3060 = 3 + 0 + 6 + 0 = 9

Since the sum of the digits of 3060 which is equal to 9 is divisible by 3, thus 3060 is divisible by 3.

3060 ÷ 3 = 1020

**Is 3060 divisible by 4: Yes**

**Explanation**

The last two digits of 3060 is equal to 60, and 60 is divisible by 4, thus 3060 is divisible by 4.

3060 ÷ 4 = 765

**Is 3060 divisible by 5: Yes**

**Explanation**

The last digit of 3060 is zero (0), thus 3060 is divisible by 5.

3060 ÷ 5 = 612

**Is 3060 divisible by 6: Yes**

**Explanation**

Since, 3060 is divisible by 2 and 3 both, thus 3060 is divisible by 6.

3060 ÷ 6 = 510

**Is 3060 divisible by 8: No**

**Explanation**

The last three digits of 3060 counting from right is equal to 060 is not divisible by 8, thus 3060 is not divisible by 8.

**Is 3060 divisible by 9: Yes**

**Explanation**

The sum of digits of 3060 = 3 + 0 + 6 + 0 = 9

Since the sum of the digits of 3060 which is equal to 9 is divisible by 9, thus 3060 is divisible by 9.

3060 ÷ 9 = 340

**Is 3060 divisible by 10: Yes**

**Explanation**

The last digit of 3060 is zero (0), thus 3060 is divisible by 10.

3060 ÷ 10 = 306

**Is 3060 divisible by 11: No**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 3060 is

= 6 + 0 – (3 + 0)

= 6 – 3 = 3

Since, the difference between the sum of digits at odd place and even place counting from right of 3060 is neither equal to zero not equal to 11, thus 3060 is not divisible by 11

**Answer** (x) 406839

**Is 406839 divisible by 2: No**

**Explanation:**

Since 406839 is not an even number, thus it is divisible by 2.

**Is 406839 divisible by 3: Yes**

**Explanation:**

The sum of digits of 406839 = 4 + 0 + 6 + 8 + 3 + 9 = 30

Since the sum of the digits of 406839 which is equal to 30 is divisible by 3, thus 406839 is divisible by 3.

406839 ÷ 3 = 135613

**Is 406839 divisible by 4: No**

**Explanation**

The last two digits of 406839 is equal to 39, and 406839 is not divisible by 4, thus 406839 is not divisible by 4.

**Is 406839 divisible by 5: No**

**Explanation**

The last digit of 406839 is neither zero (0) nor five (6), thus 406839 is not divisible by 5.

**Is 406839 divisible by 6: No**

**Explanation**

Since, 406839 is not divisible by 2 and divisible by 3, thus 406839 is not divisible by 6.

**Is 406839 divisible by 8: No**

**Explanation**

The last three digits of 406839 counting from right is equal to 839 is not divisible by 8, thus 406839 is not divisible by 8.

**Is 406839 divisible by 9: No**

**Explanation**

The sum of digits of 406839 = 4 + 0 + 6 + 8 + 3 + 9 = 30

Since the sum of the digits of 406839 which is equal to 30 is not divisible by 9, thus 406839 is not divisible by 9.

**Is 406839 divisible by 10: No**

**Explanation**

The last digit of 406839 is not zero (0), thus 406839 is not divisible by 10.

**Is 406839 divisible by 11: No**

**Explanation**

The difference between the sum of digits at odd place and even place counting from right of 406839 is

= 9 + 8 + 0 – (3 + 6 + 4)

= 17 – 13 = 4

Since, the difference between the sum of digits at odd place and even place counting from right of 406839 is neither equal to zero not equal to 11, thus 406839 is not divisible by 11