Prime Factorisation

Here’s how to express any number as prime factors.

When you do factorisation of any number, you get prime numbers as well as composite numbers as factors.

Composite numbers are those that can be expressed as products of prime numbers. For example, 35 and 70 are composite numbers and can be expressed as 35=7×5 and 70=7x5x2.

Read more on Factors and factorisation

Prime factorisation means expressing any number as the product of only prime numbers (no composite numbers to be included).

Prime factorisation can be done by two methods – factor tree method and successive division method.

Prime Factorisation using factor tree method

Lets take the example of number 240 and carry out its prime factorisation. Here are the steps.

1. Start with the smallest prime factor of the number. So, 240=2×120.
2. Next, find the smallest prime factor of 120. Continue to find the smallest prime factor at every step. Stop when the last row has only prime numbers left.

So, 240=2×120.

240=2×120.

240=2x2x60.

240=2x2x2x30.

240=2x2x2x2x15.

240=2x2x2x2x3x5.

Thus, prime factorisation of 240 = 2 x 2 x 2 x 2 x 3 x 5

The result will be the same even if the factor tree branches out differently.

Prime Factorisation using successive method

Using this method, we divided the number successively by the smallest prime number possible till we get the quotient as 1.

Divide the number 240 by the smallest prime number 2. Write the quotient below the dividend. Continue doing this till the quotient is 1.

Thus, 240 = 2 x 2 x 2 x 2 x 3 x 5