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Determine if 25110 is divisible by 45.

Determine if 25110 is divisible by 45.

Grade:12th pass

3 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
16 days ago
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.
Sailikith Nallabirudu
57 Points
9 hours ago
As the sum of the digits of 25110 is divisible by 9, therefore, 25110 is divisible by 9. Since the number is divisible by 5 and 9 both, it is divisible by 45.
Ayush Kumar
32 Points
6 hours ago
If you want to check the divisibility of any number (in this case 25110) from any particular number(in this case 45)
then break the divisor into factors and check its divisibilty with that dividend.
Factors of 45=3*3*5
Check the divisibilty of the dividend from this small number 
for checking a number divisibilty from 3 just add the digits of the dividend and check if the sum is divisible by 3,
now the other factor is 5 for checking a number’s divisibilty by 5 just check its unit digit number if that unit digit is 5 or 0 then it is divisibilty by 5 otherwise not
so in this case  25110 the sum of digits is 2+5+1+1+0
and the unit digit is 0 therefore this number is divisible by 45 

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