🔁 Remainders
4 exam question types, fully solvedRemainders are the most asked number-theory topic in SSC. The whole skill is one idea: you never need the big number — only its remainder.
Rule 1 — Work with the remainder, not the number. For a sum, product, square, or power, replace each number by its remainder and do the same operation. If the answer comes out bigger than the divisor, divide once more so it ends up smaller.
Example: a number leaves remainder 6 with 7. Its square leaves 6² = 36, and 36 ÷ 7 leaves 1. Done — no need to know the number itself.
Rule 2 — “Same remainder” questions use HCF or LCM.
• Greatest number dividing several numbers with the same remainder = HCF of their differences.
• Least number leaving the same remainder r with several divisors = LCM + r.
Power trick: for a big power, find a small power that gives remainder 1 or −1, then split the big power into those.
A number leaves remainder 6 with 7. Its square leaves remainder with 7. For Rem(19 × 23 ÷ 6): use 1 × 5 = 5 → remainder .
Q1What is the remainder when 2⁵⁰ is divided by 7?
Q2A number leaves remainder 4 when divided by 5. What remainder does its square leave when divided by 5?
Q3Find the greatest number that divides 60 and 75 leaving the same remainder.
Real exam questions — Remainders
4 question types · 12 solved examples from real SSC papersRemainders are the single most common number-theory theme in SSC papers. Master these four shapes and you cover almost every remainder question.
When 888 is divided by 35, what is the remainder?
What is the remainder when 3⁸ is divided by 7?
Two numbers leave remainders 17 and 9 when divided by 23. What is the remainder when their sum is divided by 23?