Prime factorisation — lesson. Mathematics CBSE, Class 6.

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Prime factorization is to write the composite number as a product of its prime factors.

Let us find the prime factor for

$12$ .

$12 = 4 \times 3$

$4$ can be written as

$2 \times 2$ .

$12 = 2 \times 2 \times 3$

Therefore, the prime factor of

$12$ is

$2 \times 2 \times 3$ .

There are two ways to find the prime factor.

1. Factor tree method

2. Division method

Factor tree method

Let's see the example using factor tree method.

Example:

Find the prime factor of

$48$ using the factor tree method.

Prime factor of

$48$

$=$

$8 \times 6$ .

Prime factor of

$8$

$=$

$4 \times 2 = 2 \times 2 \times 2$ .

Prime factor of

$6$

$=$

$3 \times 2$ .

The ending prime numbers are the prime factors.

Therefore, the prime factor of

$48$

$=$

$2 \times 2 \times 2 \times 2 \times 3$ .

Division method:

Step 1: Write the given number.

Step 2: Start with the lowest prime number, which exactly divides the given number.

Step 3: Write that lowest prime number on the left side of the given number.

Step 4: Write down the quotients in the next line of the given number.

Step 5: Repeat the process until you get

$1$ as a quotient.

Step 6: The prime numbers you obtained on the left side of the given number is prime factors.

Example:

Find the prime factor of

$27$ using division method.

Write a pair of factors.

$27 = 9 \times 3$

Now further factorize the composite factor

$9$ as

$3$ and

$3$ .

Repeat the process till you get the prime factors of all the composite factors.

Since the last number

$3$ is a prime number, we cannot factorize it further.

Therefore, the prime factor of

$27$

$=$

$3 \times 3 \times 3$ .

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3. Prime factorisation

Theory: