Example 1 · level 1
Find the HCF of 40 and 36 using prime factorisation.
Show solution
- 40 = 2 × 2 × 2 × 5
- 36 = 2 × 2 × 3 × 3
- Common part: 2 × 2 = 4.
Answer: 4
CLASS 10 MATHS · REAL NUMBERS
HCF and LCM by prime factorisation
HCF = product of the smallest powers of common primes. LCM = product of the greatest powers of all primes. For two numbers, HCF × LCM = product.
Loading practice…
Worked examples
Example 2 · level 2
Find the HCF of 16, 10, 36 by prime factorisation.
Show solution
- 16 = 2 × 2 × 2 × 2
- 10 = 2 × 5
- 36 = 2 × 2 × 3 × 3
- HCF = 2 = 2.
Answer: 2
Example 3 · level 3
The HCF of two numbers is 9 and their LCM is 108. If one number is 27, find the other.
Show solution
- HCF × LCM = 9 × 108 = 972.
- Other number = 972 ÷ 27 = 36.
Answer: 36