Find which of the following numbers are divisible by 2:
(i) 352
(ii) 523
(iii) 496
Answer
According to the divisibility of 2, if the unit digit of the number is zero or an even number then the number is divisible by 2.
(i) 352 — Last digit is 2 (even number).
(ii) 523 — Last digit is 3 (odd number).
(iii) 496 — Last digit is 6 (even number).
Hence, 352 and 496 are divisible by 2.
Find which of the following numbers are divisible by 4:
(i) 222
(ii) 532
(iii) 678
Answer
According to the divisibility of 4, if the two digit number formed by its ten's digit and unit digit is divisible by 4 then the number is divisible by 4.
(i) 222 — Last 2 digits are 22 and 22 is not divisible by 4.
(ii) 532 — Last 2 digits are 32 and 32 is divisible by 4.
(iii) 678 — Last 2 digits are 78 and 78 is not divisible by 4.
Hence, 532 is divisible by 4.
Find which of the following numbers are divisible by 8:
(i) 324
(ii) 2536
(iii) 92760
Answer
According to the divisibility of 8, if the number formed by its hundred's, ten's and unit digits is divisible by 8 then the number is divisible by 8.
(i) 324 — Last 3 digits are 324 and 324 is not divisible by 8.
(ii) 2536 — Last 3 digits are 536 and 536 is divisible by 8.
(iii) 92760 — Last 3 digits are 760 and 760 is divisible by 8.
Hence, 2536 and 92760 are divisible by 8.
Find which of the following numbers are divisible by 3:
(i) 221
(ii) 543
(iii) 28492
Answer
According to the divisibility of 3, if the sum of the digits of the number is divisible by 3 then the number is divisible by 3.
(i) 221 = 2 + 2 + 1 = 5. And 5 is not divisible by 3.
(ii) 543 = 5 + 4 + 3 = 12. And 12 is divisible by 3.
(iii) 28492 = 2 + 8 + 4 + 9 + 2 = 25. And 25 is not divisible by 3.
Hence, 543 is divisible by 3.
Find which of the following numbers are divisible by 9:
(i) 1332
(ii) 53247
(iii) 4968
Answer
According to the divisibility of 9, if the sum of the digits of the number is divisible by 9 then the number is divisible by 9.
(i) 1332 = 1 + 3 + 3 + 2 = 9. And 9 is divisible by 9.
(ii) 53247 = 5 + 3 + 2 + 4 + 7 = 21. And 21 is not divisible by 9.
(iii) 4968 = 4 + 9 + 6 + 8 = 27. And 27 is divisible by 9.
Hence, 1332 and 4968 are divisible by 9.
Find which of the following numbers are divisible by 6:
(i) 324
(ii) 2010
(iii) 33278
Answer
According to the divisibility of 6, if the number is divisible by 2 and 3 both then the number is divisible by 6.
(i) 324
Last digit is 4, hence 324 is divisible by 2.
3 + 2 + 4 = 9, 9 is divisible by 3. So, 324 is divisible by 3.
Hence, 324 is divisible by 6.
(ii) 2010
Last digit is 0, hence 2010 is divisible by 2.
2 + 0 + 1 + 0 = 3, 3 is divisible by 3. So, 2010 is divisible by 3.
Hence, 2010 is divisible by 6.
(iii) 33278
Last digit is 8, hence 33278 is divisible by 2.
3 + 3 + 2 + 7 + 8 = 23, 23 is not divisible by 3. So, 33278 is not divisible by 3.
Hence, 33278 is not divisible by 6.
Hence, 324 and 2010 are divisible by 6.
Find which of the following numbers are divisible by 5:
(i) 5080
(ii) 66666
(iii) 755
Answer
According to the divisibility of 5, if the unit digit is 0 or 5 then the number is divisible by 5.
(i) 5080 — Last digit is 0.
(ii) 66666 — Last digit is 6.
(iii) 755 — Last digit is 5.
Hence, 5080 and 755 are divisible by 5.
Find which of the following numbers are divisible by 10:
(i) 9990
(ii) 0
(iii) 847
Answer
According to the divisibility of 10, if the unit digit is 0 then the number is divisible by 10.
(i) 9990 — Last digit is 0.
(ii) 0 — is divisible by 10.
(iii) 847 — Last digit is 7.
Hence, 9990 and 0 are divisible by 10.
Find which of the following numbers are divisible by 11:
(i) 5918
(ii) 68717
(iii) 3882
Answer
According to the divisibility of 11, if the difference between the sum of its digits in odd places and the sum of its digits in even places is either 0 or divisible by 11 then the number is divisible by 11.
(i) 5918 — the sum of its digits in odd places = 8 + 9 = 17 the sum of its digits in even places = 1 + 5 = 6 The difference = 17 - 6 = 11 (divisible by 11).
(ii) 68717 — the sum of its digits in odd places = 7 + 7 + 6 = 20 the sum of its digits in even places = 1 + 8 = 9 The difference = 20 - 9 = 11 (divisible by 11).
(iii) 3882 — the sum of its digits in odd places = 2 + 8 = 10 the sum of its digits in even places = 8 + 3 = 11 The difference = 10 - 11 = -1 (not divisible by 11).
Hence, 5918 and 68717 are divisible by 11.
Find which of the following numbers are divisible by 15:
(i) 960
(ii) 8295
(iii) 10243
Answer
According to the divisibility of 15, if the number is divisible by 3 and 5 both then the number is divisible by 15.
(i) 960
Last digit is 0, hence 960 is divisible by 5.
9 + 6 + 0 = 15, 15 is divisible by 3. So, 960 is divisible by 3.
Hence, 960 is divisible by 15.
(ii) 8295
Last digit is 5, hence 8295 is divisible by 5.
8 + 2 + 9 + 5 = 24, 24 is divisible by 3. So, 8295 is divisible by 3.
Hence, 8295 is divisible by 15.
(iii) 10243
Last digit is 3, hence 10243 is not divisible by 5.
Hence, 10243 is not divisible by 15.
Hence, 960 and 8295 are divisible by 15.