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Class 6 Prime Time: cheat sheet
CBSE Mathematics. Factors and multiples, prime and composite numbers, divisibility tests, prime factorisation, and the HCF and LCM.
Key ideas
- A factor divides a number exactly; a multiple is the number times 1, 2, 3, …
- A prime has exactly two factors, 1 and itself. 1 is neither prime nor composite; 2 is the only even prime.
- Co-prime numbers have no common factor other than 1, such as 8 and 15.
- Divisible by 2: last digit even. By 3 or 9: digit sum divisible by 3 or 9. By 5: ends in 0 or 5. By 10: ends in 0.
- Divisible by 4: last two digits divisible by 4. By 8: last three digits divisible by 8.
- The HCF (largest common factor) solves “largest equal piece or tile”; the LCM (smallest common multiple) solves “when do they meet again”.
Remember
| Prime factorisation | 60 = 2 × 2 × 3 × 5 |
| HCF and LCM of two numbers | HCF × LCM = product of the numbers |
| Example | HCF(320, 280) = 40; LCM(4, 6) = 12 |
Watch out
- Calling 1 a prime number.
- Mixing up factors (fewer, smaller) and multiples (endless, larger).
- Using the LCM for a tiling problem (it needs the HCF).
Worked example
A room is 320 cm by 280 cm. What is the largest square tile that fits exactly along both sides, and how many such tiles cover the floor?
Working: HCF of 320 and 280 = 40; (320 ÷ 40) × (280 ÷ 40) = 8 × 7 = 56
Answer: 40 cm tiles; 56 tiles
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