Question

Determine if 11565 is divisible by 45. Hint: 5 and 9 are co-prime numbers Test the divisibility of number by (5 and 9).
​

Answer 1

Answer:

We have

45 = 3 × 3 × 5

So, 45 = 5 × 9

Let’s check if 25110 is divisible by 5

Since 25110 has 0 as its unit digit, therefore, 25110 is divisible by 5.

Let’s find the sum of the digits

$\sf \pink{2+5+1+1+0 = 9}$

Since 9 is divisible by 9

Therefore, 25110 is also divisible by 9

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

Thus, 25110 is divisible by 45

Hence, This is Answer.

Answer 2

45 = 5 × 9

1, 5 are factors of 5

1, 3, 9 are factors of 9

Hence, 5 and 9 are co-prime numbers

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

Sum of digits 25110

2 + 5 + 1 + 1 + 0

= 9

Since, the sum of digits of 25110 is divisible by 9. Hence, 25110 is divisible by 9

Since the number is divisible by both 5 and 9

Therefore 25110 is divisible by 45