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# How to Find Prime Factorization by Division Method?

August 31, 2022
written by Azhar Ejaz

There are distinct methods for the prime factorization of a number. The most common way that is used for prime factorization is given below:

• Prime factorization by factor tree method
• Prime factorization by division method

## Prime factorization by division method

The division method can also be used to determine the prime factors of a greater number by dividing the number by prime numbers. Let us learn how to determine the prime factors of a number by the division method using the following example.

For example: Find the prime factorization of 60 with the division method.

Solution:

Step 1: Divide the number by the smallest prime number such that the smallest prime number divides the number completely. Here we divide 60 by 2 to obtain 30.

Step2: Again, divide the quotient of step 1 by the smallest prime number. S0, 30 is again divided by 2 and we obtain 15.

Step 3: Repeat step 2, until the quotient becomes 1. Now, 15 is not divisible by 2, so we take the next prime number which is 3. And 15 Ã· 3 = 5. Then we divide 5 Ã· 5 = 1. Since we get 1 as the quotient, we stop here.

Step 4: Finally, multiply all the prime factors that are the divisors. Prime factorization of 60 = 2 Ã— 2 Ã— 3 Ã— 5

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