Number System
About 6 min · Numerical Ability · English
Time worked out from the lesson's 344 words at 150 words a minute, plus a minute for each question.
Mastering HCF/LCM, divisibility rules, and fraction-decimal conversions will significantly speed up your calculations across the entire Numerical Ability section.
Key ideas
- HCF (Highest Common Factor): The largest number that divides two or more numbers exactly. Also called GCD. Used when dividing things into equal groups or finding common measurements.
- LCM (Least Common Multiple): The smallest number that is divisible by two or more numbers. Used for problems involving repetition, cycles, or finding when events coincide.
- HCF × LCM = Product of two numbers: This relationship holds only for two numbers.
- Co-prime numbers: Two numbers with HCF = 1. Example: 8 and 15 are co-prime.
- Divisibility rules: Shortcuts to check if a number is divisible by 2, 3, 4, 5, 6, 8, 9, 11 without actual division.
Watch out for
- Confusing HCF and LCM formulas for fractions → Remember: HCF uses HCF on top and LCM below; LCM uses LCM on top and HCF below. Think "opposite operations."
- Applying HCF × LCM = Product formula to three or more numbers → This formula works ONLY for exactly two numbers. For three numbers, you need a different approach.
- Forgetting to check both conditions for divisibility by 6 → A number must be divisible by BOTH 2 AND 3 to be divisible by 6. Checking only one condition leads to wrong answers.
Quick reference
- HCF × LCM = Product (only for 2 numbers)
- Divisible by 3: digit sum divisible by 3
- Divisible by 4: last 2 digits divisible by 4
- Divisible by 8: last 3 digits divisible by 8
- Divisible by 11: (sum of odd-position digits) − (sum of even-position digits) divisible by 11
Check yourself: 3 questions
1. The HCF of two numbers is 12 and their LCM is 360. If one of the numbers is 60, what is the other number?
2. A number when divided by 357 leaves a remainder of 5. What will be the remainder when the same number is divided by 17?
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 18 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.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.