IBPS Clerk · Bite-size lessons
Number System
About 6 min · Numerical Ability · English
Time worked out from the lesson's 381 words at 150 words a minute, plus a minute for each question.
Number System forms the backbone of Quantitative Aptitude in IBPS Clerk Prelims. While direct questions may seem few, the concepts—HCF, LCM, divisibility, factors, and surds—underpin simplification, data interpretation, and word problems throughout the paper. Mastering this topic gives you speed advantages across multiple question types.
Key ideas
- HCF (Highest Common Factor): The largest number that divides two or more numbers exactly. Used when you need to "reduce" or find the greatest common measure (e.g., cutting ropes into equal pieces).
- LCM (Least Common Multiple): The smallest number divisible by all given numbers. Used when events repeat or align (e.g., bells ringing together, circular track meetings).
- HCF × LCM = Product of two numbers: This identity holds only for exactly two numbers—a frequent exam trap.
- Prime Factorization: Express a number as a product of primes (e.g., 60 = 2² × 3 × 5). This unlocks HCF, LCM, and factor-count problems instantly.
- Divisibility Rules: Shortcuts to check if a number divides another without actual division. Critical for simplification speed.
Watch out for
- Using HCF × LCM = Product for three or more numbers → This formula works only for exactly two numbers. For three numbers, use prime factorization separately for HCF and LCM.
- Confusing when to use HCF vs LCM in word problems → "Greatest/largest that divides" signals HCF. "Smallest that is divisible by" or "events occurring together" signals LCM.
- Forgetting +1 in factor formula → If 60 = 2² × 3 × 5, factors = (2+1)(1+1)(1+1) = 12, not 2 × 1 × 1 = 2. Each exponent needs +1.
Quick reference
- HCF: Take lowest powers; LCM: Take highest powers of all primes
- HCF × LCM = Product (only for 2 numbers)
- Factors of N = p^a × q^b → (a+1)(b+1)
- Divisibility by 11: (Sum of odd-position digits) − (Sum of even-position digits) divisible by 11
- Rationalize: Multiply top and bottom by conjugate surd
Check yourself: 3 questions
1. The HCF and LCM of two numbers are 12 and 360 respectively. If one of the numbers is 60, what is the other number?
2. Find the least number which when divided by 15, 20, and 35 leaves a remainder of 8 in each case.
3. The sum of two numbers is 216 and their HCF is 27. How many such pairs of numbers are possible?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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