Prime Factorization Meaning And Examples

Prime Factorization will be discussed in this article. And before I go deep into it, there is a need for you to understand what prime numbers are and factors. These are the two numbers that make up prime factorization.

Factor = a number that divides evenly into another number. Said differently, a number that can divide another number without given a reminder. For example, 3 is a factor of 15 because if you divide 15 by 3 (15/3), it will give 5 without any reminder.

Prime number = any number where the only factors are 1 and itself (Example: 5 is a prime number. There is no other number other than 1 and 5 you can divide it by that will give you a whole number). Note 1 is not a prime number.

Having understood prime numbers and factors, then prime factorization is breaking a number into the primes i.e. prime numbers that are multiplied to get the original number. For example, Prime factorization of 75 is 5 x 5 x 3 = 52 x 3

Every number has a prime factorization while prime numbers have 1 and themselves as their only factors. Some of the most important applications of the prime factorization are HCF (Highest Common Factors) and LCM (Lowest Common Factors).

Read: Are all integers rational numbers

How to Find Prime Factorization Of A Number

For quick understanding, use a division method to solve it. Below are the steps to follow to be able to use the division method. 

  • Step 1: Find the smallest prime number that can divide the number completely without leaving a reminder.
  • Step 2: Similarly, divide the quotient of step 1 by the smallest prime number.
  • Step 3: Repeat step 2, until the quotient becomes 1.
  • Step 4: Finally, multiply all the prime factors that are the divisors.

For example, what are the prime factors of 60


The smallest prime number that can divide 60 completely is 2. 60/2 = 30. After that you will find another smallest prime number that can divide 30 completely. It is still 2, 30/2 = 15.  Another smallest prime number that can divide 15 is 3, 15/3 = 5. Finally divide by 5 because 5 is the smallest number that can divide 5 without given a reminder.


The divisors are 2, 2, 3, 5 which will then multiply each other = 2 x 2 x 3 x 5

So, the prime factorization of 60 = 2 x 2 x 3 x 5 = 22 x 3 x 5

Read: Factors and prime factors of 24, 28, 40, 42, 45, 56

Bolarinwa Olajire

A tutor with a demonstrated history of working in the education industry. Skilled in analytical skills. Strong education professional with a M. SC focused in condensed matter. You can follow me on Twitter by clicking on the icon below to ask questions.

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