Is 9 a factor of 56a+12b?

Answer 1

To determine if 9 is a factor of 56a + 12b, we need to check if the sum of the digits of 56a + 12b is divisible by 9. Let's break it down:

56a + 12b = (5 + 6)a + (1 + 2)b = 11a + 3b

Now we need to check if 11a + 3b is divisible by 9.

In order to be divisible by 9, the sum of the digits of 11a + 3b must also be divisible by 9.

Since the digits of multiples of 11 range from 0 to 9, and the digits of multiples of 3 range from 0 to 9, the sum of the digits of 11a + 3b will always be between 0 and 18.

Therefore, 11a + 3b is not guaranteed to be divisible by 9.

In conclusion, 9 is not necessarily a factor of 56a + 12b.