Determine if 25110 is divisible by 45.
[Hint: 5 and 9 are co-prime numbers. Test the divisibility of the number by 5 and 9].

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Detailed Solution

5 and 9 are co-prime numbers. So the number divisible by both 5 and 9 is also divisible by its product 45.

By the divisibility rule of 5, we know that,
If the last number is either 0 or 5, the entire number is divisible by 5.

The last digit of 25110 is 0.
So, it is divisible by 5

By the divisibility rule of 9, we know that,
If the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.

Whereas the sum of digits 25110 is 2 + 5 + 1 + 1 + 0 = 9
Therefore, the sum of digits, 25110 is divisible by 9. So, 25110 is divisible by 9

Here the number is divisible by both 5 and 9. As 5 and 9 are co-primes, the number 25110 is divisible by 45.

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