NCERT exercise 3.3 solution part:2 class six math
In question number 2 of NCERT Exercise 3.3 class six math, tests of divisibility by 4 and 8 are to be performed for the given numbers. On the basis of the rule of divisibility by 4 and 8, the numbers given in the question have been tested for divisibility. We know that if the last two digits forming a number is divisible by 4, then the number is divisible by 4. Similarly, if the last three digits of a number is divisible by 8, then the number is divisible by 8 also.
Question (2) Using divisibility tests, determine which of the following numbers are divisible by 4; by 8:
(a) 572
Answer
Divisible by 4: Yes. 572 is divisible by 4
Divisible by 8: No. 572 is not divisible by 8
Explanation
If the last two digits of a number is divisible by 4, then the number is divisible by 4.
In the given number 572, the last two digits 72 is divisible by 4, thus 572 is divisible by 4.
The divisibility of 572 by 8 can be test by actual division. 572 is not divisible by 8.
(b) 726352 (Is 726352 divisible by 4 and 8?)
Answer
Divisible by 4: Yes (726352 is divisible by 4)
Reason: Since, the last two digits forming 726352 which is equal to 52 is divisible by 4, thus 726352 is divisible by 4.
726352 ÷ 4 = 181588
Divisible by 8: Yes (726352 is divisible by 8)
Reason: Since, the last three digits forming 726352 which is equal to 352 is divisible by 8, thus 726352 is divisible by 8.
726352 ÷ 8 = 90794
(c) 5500 (Is 5500 divisible by 4 and 8?)
Answer
Divisible by 4: Yes (5500 is divisible by 4)
5500 ÷ 4 = 1375
Explanation: If last two digits forming a number is two zeros (00) or divisible by 4, then the number is divisible by 4.
Since, the last two digits forming 5500 is double zero (00), thus 5500 is divisible by 4.
Divisible by 8: No. (5500 is not divisible by 8)
Explanation Since, the last three digits forming 5500 is not divisible by 8, thus 5500 is not divisible by 8.
(d) 6000 (Is 6000 divisible by 4 and 8?)
Answer
Divisible by 4: Yes
Explanation
Since, 6000 has last two digits are zeros, thus 6000 is divisible by 4.
6000 ÷ 4 = 1500
Divisible by 8: Yes
Explanation
Since, 6000 has last three digits are zeros, thus 6000 is divisible by 8.
6000 ÷ 8 = 750
(e) 12159 (Is 12159 divisible by 4 and 8?)
Answer
Divisible by 4: No
Explanation
Since, 12159 is an odd number, thus not divisible by 4.
Divisible by 8: No
Explanation
Since, 12159 is an odd number, thus not divisible by 8.
(f) 14560 (Is 14560 divisible by 4 and 8?)
Divisible by 4: Yes
Explanation
Since, last two digits of 14560 is divisible by 4, thus it is divisible by 4.
14560 ÷ 4 = 3640
Divisible by 8: Yes
Explanation
Since, last three digits of 14560 is divisible by 8, thus it is divisible by 8.
14560 ÷ 8 = 1820
(g) 21084 (Is 21084 divisible by 4 and 8?)
Answer
Divisible by 4: Yes
Explanation
Since, last two digits of 21084, which is equal to 84, is divisible by 4, thus it is divisible by 4.
21084 ÷ 4 = 5271
Divisible by 8: No
Explanation
Since, last three digits of 21084 is not divisible by 8, thus it is not divisible by 8.
(h) 31795072 (Is 31795072 divisible by 4 and 8?)
Divisible by 4: Yes
Explanation
Since, last two digits of 31795072, which is equal to 72, is divisible by 4, thus it is divisible by 4.
31795072 ÷ 4 = 7948768
Divisible by 8: Yes
Explanation
Since, last two digits of 31795072, which is equal to 072, is divisible by 8, thus it is divisible by 8.
31795072 ÷ 4 = 3974384
(i) 1700 (Is 1700 divisible by 4 and 8?)
Divisible by 4: Yes
Explanation
Since, last two digits of 1700 are zeros, thus it is divisible by 4.
1700 ÷ 4 = 425
Divisible by 8: No
Explanation
Since, last three digits of 1700, which is equal to 700, is not divisible by 8, thus it is not divisible by 8.
(j) 2150 (Is 2150 divisible by 4 and 8?)
Answer
Divisible by 4: No
Explanation
Since, last two digits of 2150 is not divisible by 4, thus it is not divisible by 4.
Divisible by 8: No
Explanation
Since, last three digits of 2150 is not divisible by 8, thus it is not divisible by 8.