HCF or GCD of Numbers

In this class, We discuss HCF or GCD of Numbers.

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Factor and Multiple:

If a number A, divide a number B exactly. We say the number A is the factor of B.

In the same case, the number B is multiple of A.

Example:

A = 6 B = 24

24/6 = 4

The number A divided B exactly.

6 is a factor of 24.

24 is a multiple of 6. The number 6 multiplied by four will give 24.

HCF or GCD of numbers

HCF means the highest common factor

GCD means greatest common divisor.

Example to understand HCF or GCD.

24, 36

Factors of 24 are 1, 2, 3, 4, 6, 8, and 12.

Factors of 36 are 1, 2, 3, 4, 6, 12, 18.

HCF means to pick the highest common factor of 24, 36.

HCF of 24, 36 is 12.

Two methods to find HCF or GCD.

1) Factorization method

2) Divison Method

Factorization method

Write each number as a product of prime factors.

Example: 24, 36

24 can be written as 2^3 * 3

36 can be written as 2^2 * 3^2

After writing prime factors, the product of least powers of common factors gives the HCF.

2^2 * 3 = 12

HCF = 12

Division Method:

Divide large numbers by small numbers.

Example: 2923, 3239

3239/2923 the reminder value is 316

Now divide the divisor by reminder. Repeat the process till the remainder value is zero.

2923/316. The remainder value is 79

316/79, the remainder is zero.

The HCF of 2923, 3239 is 79.