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UPSC Prelims

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CSAT 2024

Q18 2024, Divisibility Rules and Remainder Theorem

421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?

421 और 427 को जब एक ही संख्या से विभाजित किया जाता है, तो समान शेषफल 1 आता है। भाजक के रूप में कितनी संख्याओं का उपयोग किया जा सकता है ताकि शेषफल 1 ही आए?

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To find the numbers that can be used as the divisor to get the same remainder of 1 when dividing 421 and 427, we can follow following steps:

Subtract the remainder ( i.e. 1) from both numbers: 421 - 1 = 420 and 427 - 1 = 426.
Prime factorize both numbers: 420 = 2^2 * 3 * 5 * 7 and 426 = 2 * 3 * 71.

Now, look for common factors in their prime factorizations:

Both have 2 as a factor.
Both have 3 as a factor.
Both have no other common factors besides 1.

So, the common divisors that would give the same remainder of 1 when dividing 421 and 427 are the factors of 6, which are 1, 2, 3, and 6.

Therefore, the correct answer is: (c) 3

व्याख्या Please wait..

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