Divisibility Rules

Tested in 3 real MPSC questions across 2 years (2018–2021). See it in context on the interactive Concept Graph →

Years it was asked

2021 2018

What you need to know first

Basic algebraDivisibility conceptsBasic DivisionPrime factorizationMultiplication principleDivisibility by 5

Real questions that test this

खालील संख्येपैकी किती संख्यांना 273 ने भाग जात नाही ? 546, 1156, 3003, 3564, 5733, 3822, 9605, 8736 How many of the following numbers are not divisible by 273 ? 546, 1156, 3003, 3564, 5733, 3822, 9605, 8736

1)5

2)3&check; Correct

3)4

4)8

To check divisibility by 273, we can check divisibility by its coprime factors 3 and 91 (or 3, 7, and 13). Testing each number helps identify how many are not divisible, resulting in the correct count of 2 numbers.

2, 3, 5, 6, 7 आणि 9 या अंकांपासून 5 ने भाग जाणारी आणि कोणतीही अंक पुन्हा न येता, अशा तीन अंकी किती संख्या तयार होऊ शकतील ? How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated ?

1)5

2)10

3)15

4)20&check; Correct

A 3-digit number is divisible by 5 if its unit's digit is 5. Given digits: 2, 3, 5, 6, 7, 9. Unit place can only be filled by '5' (1 way). The remaining 2 places can be filled from the remaining 5 digits (2, 3, 6, 7, 9) in 5P2 = 5 * 4 = 20 ways. Total numbers = 1 * 20 = 20.

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