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?
Read this question in English
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?
(a) 1 · (b) 2 · (c) 3 · (d) 4
उत्तर और व्याख्या · explanation in English
Answer: (c) 3
If both numbers leave remainder 1, the divisor divides 420 and 426, and hence their HCF, 6. The divisors of 6 that are greater than 1 are 2, 3 and 6, so three numbers work (1 cannot leave a remainder of 1).
- Remainder 1 means the divisor divides 421 − 1 = 420 and 427 − 1 = 426.
- HCF(420, 426) = HCF(420, 6) = 6.
- Divisors of 6 are 1, 2, 3 and 6. A divisor must be larger than the remainder, so 1 is ruled out.
- Possible divisors: 2, 3 and 6, i.e. 3 numbers.
- Check: 421 = 6 × 70 + 1 and 427 = 6 × 71 + 1.
Remember · Same remainder r: the divisor divides each number minus r. Count the HCF’s divisors that are larger than r.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·