# Highest Common Factor (HCF)

### Factor

A factor is a number which divides the dividend without remainder. If there is no remainder then both divisor and quotient are factors of the dividend.

### Example

Divide 20 by 4

divisor = 4

quotient = 5

remainder = 0

In this case both 4 and 5 are factors of the number 20.

### Common Factor

A factors that are common to two or more numbers are said to be common factors. 1 is the common factor of all the numbers.

### Co-Primes

If a set of numbers have only one factor as common factor (the number 1) then that set of numbers are called co-primes.

### HCF

H.C.F of two or more numbers is the biggest number that can exactly divide all the given numbers without remainder.

Highest Common Factor (HCF) also called as Greatest Common Divisor(GCD).

### Example: HCF of 10 and 15

Factors of 10: 1, 2, 5

Factors of 15: 1, 3, 5

Common factors of 10 and 15 : 1, 5

HCF of 10 and 15: 5

### Finding HCF using Factorization Method

1. Find prime factors of the given numbers.

2. Find prime factors common to all the numbers.

3. The HCF is the product of the common prime factors.

### Example: HCF of 24 and 30

Prime factors of 24: 1, 2, 2, 2, 3

Prime factors of 30: 1, 2, 3, 5

Common prime factors: 1, 2, 3

HCF = 1 * 2 * 3 = 6

### Uses

HCF is used to simplify a fraction. The fraction 24/30 can be simplified by dividing both numerator and denominator by the HCF 6.