# 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 = 5^{2} 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

Solution

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.

divisors | quotient |

2 | 60 |

2 | 30 |

3 | 15 |

5 | 5 |

1 |

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 = 2^{2} x 3 x 5

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