Question

If a679b is a five digit number in base 10 and is divisible by 72 ,then the value a + b is

Answer 1

Factors of 72= 9 x8
so check the divisibilty by 9 first
[a + 6 +7 + 9 + b]= mod 9
[a + 13 +b]= mod 9
[a +b]= 13-9
a +b= 5

now check the divisibility by 8 
we get a= 2

putting the value of a in a+b=5 we get the value of b which is b= 2
so the number is 36792

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