Prime factorisation is the process of finding the prime factors of a given number. Prime factors are the prime numbers that divide the given number exactly without leaving any remainder.

To perform prime factorisation, follow these steps:

1. Divide the given number by the smallest prime number that divides it exactly. If the number is not divisible by any prime number, then it is a prime number itself.


2. Repeat step 1 with the quotient obtained in step 1 until the quotient becomes a prime number.


3. Write all the prime numbers obtained in step 1 as factors of the given number.

For example, let's find the prime factorisation of 240.

Step 1: Divide 240 by 2, which gives 120. 2 is a prime number, so we write it down as a factor of 240.

Step 2: Divide 120 by 2, which gives 60. 2 is a prime number, so we write it down as a factor of 240.

Step 3: Divide 60 by 2, which gives 30. 2 is a prime number, so we write it down as a factor of 240.

Step 4: Divide 30 by 2, but it is not divisible by 2. So, we divide it by the next prime number, which is 3. 30 divided by 3 gives 10. 3 is a prime number, so we write it down as a factor of 240.

Step 5: Divide 10 by 2, but it is not divisible by 2. So, we divide it by the next prime number, which is 5. 10 divided by 5 gives 2. 5 is a prime number, so we write it down as a factor of 240.

Step 6: 2 is a prime number, so we write it down as a factor of 240.

Therefore, the prime factorisation of 240 is 2 x 2 x 2 x 2 x 3 x 5.



To find the square root of a number using prime factorisation, follow these steps:

1. Find the prime factorisation of the given number.


2. Pair up the factors in twos, starting from the left. If there is a single factor left at the end, pair it with itself.


3. Multiply each pair of factors together.


4. The product obtained in step 3 is the square root of the given number.

For example, let's find the square root of 4802.

Step 1: Find the prime factorisation of 4802.

4802 = 2 x 7 x 17 x 17

Step 2: Pair up the factors in twos starting from the left.

(2 x 17) and (7 x 17)

Step 3: Multiply each pair of factors together.

2 x 17 = 34

7 x 17 = 119

Step 4: The product obtained in step 3 is the square root of the given number.