# Factors and multiples

## Factors and multiples

### HCF (Highest Common Factor) or G.C.D. (Greatest Common Divisor)

The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly and that is always smaller or equal to those numbers. So, H.C.F (Highest Common Factor). is the divisor. (or factor) HCF or GCD of two or more numbers is the greatest number that divides each one of them exactly.

### Methods of finding the H.C.F. of a given set of numbers.

Prime Factors

A factor of a given number is called a prime factor if this factor is a prime number.

### Example

The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. Out of these 2, 3 and 7 are prime numbers. Therefore, 2, 3 and 7 are the prime factors of 42.

### Prime Factorization Method:

Express each one given numbers as the product of prime factors. The product of least powers of common prime factors gives H.C.F.

### Prime Factorization Method :

Suppose we have to find the H.C.F. of two or more numbers.

Step 1. Express each one of the given numbers as the product of prime factors.

Step 2. The product of terms containing least powers of common prime factors gives the H.C.F. of the given numbers.

### Long Division Method :

Suppose we to find the H.C.F. of two given numbers.

Step 1. Divide the larger number by smaller one.

Step 2. Divide the divisor by the remainder.

Step 3. Repeat the process of dividing the preceding divisor by the remainder last obtained, till remainder 0 is obtained.

Then, the last divisor is the required H.C.F.

Now, H.C.F. of three numbers = H.C.F. of [(H.C.F. of any two) and the third]

### H.C.F. of three given numbers:

H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given numbers.

Similarly, the H.C.F. of more than three numbers may be obtained.