Determine if 25110 is divisible by 45.

Determining the divisibility of a dividend is easy if the divisor is broken into its factors. If we try to check for divisibility by 45 itself, it might lead to a complex calculation. So, it is advised to break 45 into its prime factors. Complete step-by-step answer: Here, we have to check the divisibility of 25110 by 45. And it is easy to determine divisibility with divisor’s prime factors, thus prime factors of divisor 45 is 45=32×5×1 Thus, prime factors of 45 are: 3,5,1... (1) Now, to determine the divisibility of 25110 by 45, we have to check its divisibility with 3,5,1, i.e., Divisibility rules of 3 and 5 will be checked on 25110, as it is already divisible by 1. Now, Divisibility rule of 3 is, if sum of all the digits of dividend is divisible by 3 or not, if it is divisible by 3 then the whole dividend is said to be divisible by 3... (2) Similarly, divisibility rule of 5 is, if the last digit of dividend is either 0 or 5, then dividend is said to be divisible by 5... (3) From combining equation (2) and (3), we can say that A dividend is said to be divisible by 45, only if it is divisible by 3 and 5. Thus, applying divisibility rule of 3 on 25110 from equation (2), we get 25110→(2+5+1+1+0)=9, which is divisible by 3 And applying divisibility rule of 5 from equation (3), we get 25110→ last digit is 0, hence it is also divisible by 5 Thus, we can say that 25110 is divisible by 3 and 5. Hence, 25110 is divisible by 45. Note: An easiest way to solve such problems is direct division of dividend through divisor. If the remainder comes out to be 0 then it can be said that dividend is divisible by divisor.