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].
Solution:
25110 is divisible by 5 because the last digit is equal to 0.
Sum of digits of 25110 = 2 + 5 + 1 + 1 + 0 = 9
Sum of digits is divisible by 9. Therefore, 25110 is divisible by 9.
Therefore, 25110 is divisible by both 5 and 9. Also, 5 and 9 are both co-prime numbers. Hence, 25110 is also divisible by their product which is equal to 45.
(If a number is divisible by two co-prime numbers then it is divisible by their product also.)
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