Question

A456b72c is divisible by 72 what is least value for a + b+ c

Answer 1

Answer:

3

Step-by-step explanation:

Being divisible by 72 is the same as being divisible by both 8 and 9.

Since 1000 is a multiple of 8, the number a456b72c is divisible by 8 only if the three digit number 72c is divisible by 8.  Since 720 is divisible by 8, this will be true only if c is divisible by 8.  So c must be either 0 or 8.

A number is divisible by 9 only if the sum of its digits is divisible by 9.  So a456b72c is divisible by 9

only if a + 4 + 5 + 6 + b  + 7 + 2 + c is divisible by 9.

Since 4+5 = 9 and 7+2 = 9, this is the same as requiring that

a + b + c + 6 be divisible by 9.

So a + b + c cannot be less than 3, and it certainly can be 3 by taking

a = 1, b = 2, c = 0.

[ P.S. The resulting number is 14562720 = 72 × 202260 ]