Determine if 25110 is Divisible by 45


Question: 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.]

If a number 'a' is divisible by all the prime factors of 'b', then 'a' is divisible by 'b'

Answer: Yes, 25110 is divisible by 45

Let's check the divisibility of 25110 by 5 and 9 using divisibility rules

Explanation:

Let's find the prime factorization of 45

Prime factorization of a number means to express the number as the product of prime factors.

45 = 3 × 3 × 5

So, 45 =  5 × 9

Let's check if 25110 is divisible by 5

Since, 25110 has 0 as it's unit digit therefore, 25110 is divisible by 5                       (If a number has 0 or 5 as it's unit digit the, the number is divisible by 5)

Now, let's check if 25110 is divisible by 9

Let's find the sum of the digits

2+5+1+1+0 = 9

Since, 9 is divisible by 9

Therefore, 25110 is also divisible by 9                        (If the sum of all the digits of a given number is a multiple of 9, the given number is also a multiple of 9)

Since, 25110 is divisible by both 5 and, it is divisible by 45

Thus, 25110 is divisible by 45