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What is the smallest number whhich must be added to 75 to make a number exactly divisible by 9?
6.
To check for divisibility by 9, add the digits of the number together and if the sum is divisible by 9, then the original number is divisible by 9.
If the test is repeated on the sum(s) until a single digit remains, then this is the remainder when the original number is divided by 9.
Subtracting this remainder from 9 will give the smallest number that needs to be added to to the original number to make it divisible by 9.
For 75:
7 + 5 = 12
1 + 2 = 3
so 75 ÷ 9 has a remainder of 3, therefore add 9 - 3 = 6 to 75 to make it divisible by 9. (75 + 6 = 81 = 9 x 9).
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