Question

If a679b is a five digit number that is divisible by 72 then a+b is equal to

Answer 1

given number=a679b
72=8×9
divisibility by 8 is last 3 digits is divisible by 8
last 3 digits=79b
so b must be 2 then 792 is divisible by 8
divisibility by 9 is sum of the numbers is divisible by 9
a+6+7+9+2=a+24
so a must be 3 then 3+24=27 is divisible by 9
therefore 36792 is divisible by 72

Answer 2

$<b><i><u>Answer :</u>$

Given, A679B a number.

Need to find out it is divisible by 72.

⇒ Prime factors of 72 = 9 and 8

So, it is enough to check the given 5-digit number is divisible by 9 and 8.

⇒ To check the number is divisible by 8 last three digits must be divisible by 8.

⇒ 79B is divisible by 8 should be checked.

⇒ Now, from divisibility rule 100b + 10c + d

We get

⇒ 100(7) + 10(9) + B = 790 + B

Substitute a number in B which satisfy the equation using trail error method

⇒ B must be 2 to be divisible by 8

⇒ 792 is divisible by 8

∴ A679B = A6792 is divisible by 8

⇒ A6792 is divisible by 9 only if sum of the given digits is divisible by 9

⇒ A + 6 + 7 + 9 + 2 = A + 24

Put a value in A which satisfy the equation

A = 3

A + 24 = 27 is divisible by 9.

∴ A679B is divisible by 72 and the values of A = 3 and B = 2

Hence, 36792 is divisible by 72

a=3

b=2

a+b=3+2=5