Question

2. Using divisibility tests, determine which of the following numbers are divisible by 3;by 4;by 5; by 6; by 8; by 9; by 10; by 11(say, yes or no) :
4; by 8
(a) 572
( 14560
(b) 726352 (c) 5500 (d) 6000
(h) 31795072 (1) 1700
(e) 12159
2150
(g) 21084​

Answer 1

Answer:

A number is divisible by 4 if the number formed by last two digits is divisible by 4. i.e tens and ones place digits.

A number is divisible by 8 if the number formed by last three digits i.e hundreds, tens and ones place digits.

i) 572

by 4: last two digits are 72 and 72 is divisible by 4. Therefore, 572 is also divisible by 4.

by 8: last three digits are 572 and 572 is not divisible by 8.

ii) 726352

by 4: last two digits are 52 and 52 is divisible by 4. Therefore, 726352 is also divisible by 4.

by 8: last three digits are 352 and 352 is divisible by 8. Therefore, 726352 is also divisible by 8.

iii) 5500

by 4: last two digits are 00 and 00 is divisible by 4. Therefore, 5500 is also divisible by 4.

by 8: last three digits are 500 and 500 is not divisible by 8. Therefore, 5500 is not divisible by 8.

iv) 6000

by 4: last two digits are 00 and 00 is divisible by 4. Therefore, 6000 is also divisible by 4.

by 8: last three digits are 000 and 000 is divisible by 8. Therefore, 6000 is divisible by 8.

v) 12159

by 4: last two digits are 59 and 59 is not divisible by 4. Therefore, 12159 is also not divisible by 4.

by 8: last three digits are 159 and 159 is not divisible by 8. Therefore, 12159 is divisible by 8.

vi) 14560

by 4: last two digits are 60 and 60 is divisible by 4. Therefore, 14560 is also divisible by 4.

by 8: last three digits are 560 and 560 is divisible by 8. Therefore, 14560 is divisible by 8.

vii) 21084

by 4: last two digits are 84 and 84 is divisible by 4. Therefore, 21084 is also divisible by 4.

by 8: last three digits are 084 and 084 is not divisible by 8. Therefore, 21084 is divisible by 8.

viii) 31795072

by 4: last two digits are 72 and 72 is divisible by 4. Therefore, 31795072 is also divisible by 4.

by 8: last three digits are 072 and 072 is divisible by 8. Therefore,31795072 is divisible by 8.

ix) 1700

by 4: last two digits are 00 and 00 is divisible by 4. Therefore, 1700 is also divisible by 4.

by 8: last three digits are 700 and 700 is not divisible by 8. Therefore, 1700 is not divisible by 8.

x) 2150

by 4: last two digits are 50 and 50 is not divisible by 4. Therefore, 2150 is also not divisible by 4.

by 8: last three digits are 150 and 150 is not divisible by 8. Therefore, 2150 is not divisible by 8.