Prime Factorization

Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers. Here, all the concepts of prime factors and prime factorization methods have been explained which will help the students understand how to find the prime factors of a number easily.

What is Prime Factorization?

Prime factorization is defined as a way of finding the prime factors of a number i.e. the prime numbers which can be multiplied together to get the original number. For example, the prime factors of 126 will be 2, 3 and 7 as 2 × 3 × 7 = 126 and 2, 3, 7 are primes.

Prime Factors of a Number

Prime factors of a number are the set of prime numbers which when multiplied by together give the actual number. It is similar to factoring a number and considering only the prime numbers among the factors. For example, the prime factors of 6 will be 2 and 3, the prime factors of 26 will be 13 and 2, etc.

Prime Factorization Method

The steps to calculate the prime factors of a number is similar to the process of finding the factors of a large number. First, the number has to be divided exactly with the least possible prime number which can be 2, 3, 5, etc. This process has to be continued until the end result is 1. Now, the prime factors of that number will be the prime numbers that have divided the number in this process.

Steps to do Prime Factorization:

Below is a detailed step by step process of prime factorization by taking 460 as an example.

    • Step 1: Divide 460 by the least prime number i.e. 2.

So, 460 ÷ 2 = 230

    • Step 2: Again Divide 230 with the least prime number (which is again 2).

Now, 160 ÷ 2 = 115

    • Step 3: Divide again with the least prime number which will be 5.

So, 115 ÷ 2 = 23

    • Step 4: As 23 is a prime number, divide it with itself to get 1.

Now, the prime factors of 460 will be 22 x 5 x 23

Prime Factorization Example Question

An example question is given below which will help to understand the process of calculating the prime factors of a number easily.

Example of Prime Factorization Method: Find the prime factors of 1240.

Steps Prime Factors Product
Step 1: Divide by 2 2 1240 ÷ 2 = 620
Step 2: Divide by 2 2 620 ÷ 2 = 310
Step 3: Divide by 2 2 310 ÷ 2 = 155
Step 4: Divide by 5 5 155 ÷ 5 = 31
Step 4: Divide by 31 31 31 ÷ 31 = 1

∴ The prime Factors of 1240 will be 22 × 5 × 31.

Prime Factorization Worksheet (Questions)

  1. What is the prime factorization of 48?
  2. Write the prime factors of 2664 without using exponents.
  3. Is 40 = 20 × 2 an example of prime factorization process? Justify.
  4. Write 6393 as a product of prime factors.

Factors and Prime Factors of Common Numbers

Factors of 36 Factors of 24
Factors of 12 Factors of 48
Factors of 72 Factors of 120
Factors of 18 Factors of 25

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Practise This Question

We have three numbers 2, 4, 7. Find the LCM of these numbers.