HCF
What is HCF?
HCF means the largest number that divides two or more numbers exactly (without leaving any remainder).
It is also called GCD (Greatest Common Divisor).
Methods to Find HCF
1. Factor Method
Write all factors of given numbers
Find the greatest common factor
Example:
HCF of 8 and 12 = 4
2. Prime Factorization Method
Break numbers into prime factors.
Example:
18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
Common primes → 2 × 3
HCF = 6
3. Division Method
Divide the larger number by the smaller
Continue until remainder becomes 0
Last divisor is the HCF
Example:
HCF of 36 and 12 = 12
Important Points for Exams
- HCF of two prime numbers = 1
- HCF of a number with itself = same number
- HCF of consecutive numbers = 1
- HCF of even and odd number = 1
Formula to Calculate HCF
HCF × LCM = Product of the two numbers
HCF = product of the two numbers/LCM