The seven-digit number 1113A8B can be divided by 4, 5, and 9 What is the sum of the digits A and B?

4

Step-by-step explanation:

This seven-digit number can be divided by 4, 5 and 9.

This means that 4, 5 and 9 are ALL factors.

Find the least common multiply (LCM) of 4, 5 and 9.

Multiples of 4: 4, 8, 12, 16, 20

Multiples of 5: 5, 10, 15, 20

Find a multiple of 9 that is also a multiple of 20. All multiples of 20 have the factors 4 and 5.

9 X 20 = 180

The seven-digit number must be a multiple of 180 to have the factor 4, 5 and 9. You can find the multiples of 180 until the number looks like 1113A8B, but there are better methods.

All multiples of 180 end in the digit "0". Therefore B = 0.

1113A80

Since 9 is one of the factors, the rules for a number divisible for 3 apply. (9 is a multiple of 3).

You know that a number is divisible by 3 when its digits add to a number divisible by 3.

Find the sum of the digits:

1+1+1+3+A+8+0 = A + 14

A + 14 must be divisible by 3.

Therefore, A has to be either 1, 4, or 7.

If A = 1

1113180 : 180 = 6184.333

If A = 4

1113480: 180 = 6186

If A = 7

1113780 : 180 = 6187.7

A = 4 because that number is divisible by 180.

Add A = 4 and B = 0.

A + B

= 4 + 0

= 4

The sum of digits A and B is 4.