Answer:
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 <u>seven-digit number must be a multiple of 180</u> 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.
