Prime Factorization

What Is Prime Factorization in Math?

Prime factorization of a number is a way of writing a number as the product of its prime factors. Thus, the meaning of prime factorization of a number is finding prime numbers which when multiplied together give us the required number.

Division Method

Step 1: Divide the given number by its smallest prime factor. Step 2: Divide the quotient obtained by its smallest prime factor. Step 3: Repeat the process until the quotient becomes 1. Step 4: Multiply all the prime factors.

How to Find Prime Factorization of a Number

The most common methods that are used for prime factorization are: Prime Factorization by Factor tree method Prime Factorization by Division method

Prime Numbers

If a prime number occurs more than once, we write it using exponents.

Factor Tree Method

In the factor tree method, we first break down the number using the smallest prime factor of the number. The composite factors obtained in the process are further broken down until we reach the prime factors. The factors of the given number written in this way look like a tree. The prime numbers obtained in the end are called leaf nodes of the factor tree.

Factor Tree Method: Steps

Step 1: Place the number 250 on top of the factor tree. Step 2: Break down the given number using its smallest prime factor. 250 = 2 X 125 Step 3: Factorize the composite factor obtained in step 2. 125 = 5 X 5

Example

The numbers 1, 2, 3, 6 are factors of the number 6. Thus, we can say that 2 and 3 are the prime factors of 6 and express 6 as 6 = 2 X 3

Prime numbers

are numbers that have only two factors, 1 and the number itself. Examples of prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, and so on.

A factor of a number

is a number that divides the given number exactly, leaving no remainder.