Question

Determine if 25110 is divisible by 45 .

Answer 1

Hint: In this particular type of question divisibility of 25110 by 45 can be checked by checking the divisibility with the co prime factors of 45 using common divisibility rules of the factors.

Complete step-by-step answer:
Prime factors of 45 = $5 \times 3 \times 3$
Thus 5 and 9 are co-primes and if 25110 is divisible by 5 and 9 then it would be divisible by 45 .
Checking if 25110 is divisible by 5
$ \to $ the last digit of 25110 is 0 which determines that it is divisible by 5 .
Checking if 25110 is divisible by 9
 $ \to $to check divisibility by 9 , we can check whether the sum of digits of 25110 is divisible by 9 .
$ \Rightarrow 2 + 5 + 1 + 1 + 0 = 9$ which is divisible by 9 .
Therefore the number 25110 is divisible by 45 .

Note: It is important to recall the common divisibility rules to solve such types of questions. Note that a pair of integers a, b will be called coprime, mutually prime or relatively prime if they have only one common factor 1. Co primes of any divisor can be used to check the divisibility of very large numbers .