## NCERT Exercise 3.3 Solution: part-3 class six math

In this section question number 3 of NCERT Exercise 3.3 has been solved. In this question given ten numbers are to be checked for divisibility by 6. If a number is divisible by 2 and 3 both, then the number is divisible by 6.

Question (3) Using divisibility tests, determine which of the following numbers are divisible by 6

(a) 297144

**Divisible by 6: Yes**

297144 ÷ 6 = 49524

**Explanation**

297144 is an even number, and hence is divisible by 2.

297144 ÷ 2 = 148572

And, sum of the digits of 297144

= 2 + 9 + 7 + 1 + 4 + 4 = 27

The sum of the digits of 297144 which is equal to 27 is divisible by 3, thus 297144 is divisible by 3.

297144 ÷ 3 = 99048

Now, since 297144 is divisible by 2 and 3 both, thus 297144 is divisible by 6 also.

Hence, 297144 is divisible by 6.

(b) 1258

**Divisible by 6: No**

**Explanation**

1258 is an even number, and hence is divisible by 2.

1258 ÷ 2 = 629

And, sum of the digits of 1258

= 1 + 2 + 5 + 8 = 16

The sum of the digits of 1258 which is equal to 16 is not divisible by 3, thus 1258 is also not divisible by 3.

Now, since 1258 is only divisible by 2 and not divisible by 3, thus 1258 is not divisible by 6.

Hence, 1258 is not divisible by 6.

(c) 4335

**Divisible by 6: No**

**Explanation**

4335 is an odd number, and hence is not divisible by 2.

And, sum of the digits of 4335

= 4 + 3 + 3 + 5 = 15

The sum of the digits of 1258 which is equal to 15 is divisible by 3, thus 4335 is also divisible by 3.

4335 ÷ 3 = 1445

Now, since 4335 is only divisible by 3 and not divisible by 2, thus 4335 is not divisible by 6.

Hence, 4335 is not divisible by 6.

(d) 61233

**Divisible by 6: No**

**Explanation**

61233 is an odd number, and hence is not divisible by 2.

And, sum of the digits of 61233

= 6 + 1 + 2 + 3 + 3 = 15

The sum of the digits of 61233 which is equal to 15 is divisible by 3, thus 61233 is also divisible by 3.

61233 ÷ 3 = 20411

Now, since 61233 is only divisible by 3 and not divisible by 2, thus 61233 is not divisible by 6.

Hence, 61233 is not divisible by 6.

(e) 901352

**Divisible by 6: No**

**Explanation**

901352 is an even number, and hence is divisible by 2.

901352 ÷ 2 = 450676

And, sum of the digits of 901352

= 9 + 0 + 1 + 3 + 5 + 2 = 20

The sum of the digits of 901352 is equal to 20 and is not divisible by 3, thus 901352 is also not divisible by 3.

Now, since 901352 is only divisible by 2 and not divisible by 3, thus 901352 is not divisible by 6.

Hence, 901352 is not divisible by 6.

(f) 438750

**Divisible by 6: Yes**

438750 ÷ 6 = 73125

**Explanation**

438750 is an even number, and hence is divisible by 2.

438750 ÷ 2 = 219375

And, sum of the digits of 438750

= 4 + 3 + 8 + 7 + 5 + 0 = 27

438750 ÷ 3 = 146250

The sum of the digits of 438750 is equal to 27 and is divisible by 3, thus 438750 is divisible by 3.

Now, since 438750 is divisible by 2 and 3 both, thus 438750 is divisible by 6.

Hence, 438750 is divisible by 6.

(g) 1790184

**Divisible by 6: Yes**

1790184 ÷ 6 = 298364

**Explanation**

1790184 is an even number, and hence is divisible by 2.

1790184 ÷ 2 = 895092

And, sum of the digits of 1790184

= 1 + 7 + 9 + 0 + 1 + 8 + 4 = 30

1790184 ÷ 3 = 596728

The sum of the digits of 1790184 is equal to 30 and is divisible by 3, thus 1790184 is divisible by 3.

Now, since 1790184 is divisible by 2 and 3 both, thus 1790184 is divisible by 6.

1790184 ÷ 6 = 298364

Hence, 1790184 is divisible by 6.

(h) 12583

**Divisible by 6: No**

**Explanation**

12583 is an odd number, and hence is not divisible by 2.

And, sum of the digits of 12583

= 1 + 2 + 5 + 8 + 3 = 19

The sum of the digits of 12583 is equal to 19 and is not divisible by 3, thus 12583 is not divisible by 3.

Now, since 12583 is neither divisible by 2 nor 3, thus 12583 is not divisible by 6.

Hence, 1790184 is not divisible by 6.

(i) 639210

**Divisible by 6: Yes**

**Explanation**

639210 is an even number, and hence is divisible by 2.

639210 ÷ 2 = 319605

And, sum of the digits of 639210

= 6 + 3 + 9 + 2 + 1 + 0 = 21

The sum of the digits of 639210 is equal to 21 and is divisible by 3, thus 639210 is divisible by 3.

639210 ÷ 3 = 213070

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

639210 ÷ 6 = 106535

Hence, 639210 is divisible by 6.

(j) 17852

**Divisible by 6: No**

**Explanation**

17852 is an even number, and hence is divisible by 2.

17852 ÷ 2 = 8926

And, sum of the digits of 17852

= 1 + 7 + 8 + 5 + 2 = 23

The sum of the digits of 17852 is equal to 23 and is not divisible by 3, thus 17852 is not divisible by 3.

Now, since 17852 is divisible by 2 but not divisible by 3 both, thus 17852 is not divisible by 6.

Hence, 17852 is divisible by 6.