Math CentralQuandaries & Queries


Question from Tulashiram:

If a× b =27000001, then what is the value of a & b ?


There are a few different possibilities for $a$ and $b$ but I think you only need one. I would look for a prime number that divides 27000001. The first few primes are easy to check.

In integer $n$ is divisible by 2 if and only if its units digit is divisible by 2.
In integer $n$ is divisible by 3 if and only if the sum of its digits is divisible by 3.
In integer $n$ is divisible by 5 if and only if its units digit is 0 or 5.

There is a test for divisibility by 7 but I think it is easier to use long division to see if 27000001 is divisible by 7. I would also use long division for divisibility by 11, 13, 17 and so on. One you find a prime that divides 27000001 you are done.



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