Prime Factorisation Method: Real Numbers Class 10 Mathematics CBSE (NCERT)

Prime Factorization is the process of breaking down a number into its prime number factors. A prime number is a number greater than 1 that has only two factors: 1 and itself (e.g., 2, 3, 5, 7, 11,13,17,19,23,29 etc.).

Step By Step Process for Prime Factorisation

1. Start with the given number.
2. Divide it by the smallest prime number (usually 2) until it is no longer divisible.
3. Move to the next smallest prime and continue dividing until you reach 1.
4. The prime numbers obtained are the prime factors.

Example of Prime Factorisation

Step 1: Start with number 38

Step 2: Let's divide it by the smallest prime number: 2

Since 38 is even, it is divisible by 2.

38 ÷ 2 = 19

Step 3: Check if 19 is a prime number.

19 is a prime number because it has only two factors: 1 and 19.

Step 4: Since we cannot divide further, we stop here.

Conclusion:

The prime factorization of 38 is: 2 × 19