How can you find all the prime factors of a number quickly and easily?
The fastest way to find all the prime factors of a number is to start with the first prime number (2), increment up through all the prime numbers until you finally have reduced your original number to all the prime numbers needed to make your original number by multiplying them all together.
For example, for the number 120 the prime factors are 2, 2, 2, 3 and 5. Which means if you multiply all the numbers of 2, 2, 2, 3 and 5 together you will get 120.
Find Prime Factors Of 120
Here is how you can calculate the prime factors of 120 step by step:
| Find Factors of 120 |
|---|
| Start with the first prime number, the number 2. |
| Can the prime number 2 be divided into 120 without leaving a remainder? |
| Yes, 2 can be divided into 120 without remainder. |
| Add the prime number 2 to the prime factor list. |
| Replace 120 with the quotient from dividing 120 by the prime number 2: |
| 120 ÷ 2 = 60 |
| Can the prime number 2 be divided into 60 without leaving a remainder? |
| Yes, 2 can be divided into 60 without remainder. |
| Add the prime number 2 to the prime factor list. |
| Replace 60 with the quotient from dividing 60 by the prime number 2: |
| 60 ÷ 2 = 30 |
| Can the prime number 2 be divided into 30 without leaving a remainder? |
| Yes, 2 can be divided into 30 without remainder. |
| Add the prime number 2 to the prime factor list. |
| Replace 30 with the quotient from dividing 30 by the prime number 2: |
| 30 ÷ 2 = 15 |
| Can the prime number 2 be divided into 15 without leaving a remainder? |
| No, 15 divided by 2 leaves a remainder of 1. |
| Increment the prime number 2 to find the next prime number: 2 + 1 = 3 |
| Is 3 a prime number? |
| Yes, 3 is a prime number. |
| Can the prime number 3 be divided into 15 without leaving a remainder? |
| Yes, 3 can be divided into 15 without remainder. |
| Add the prime number 3 to the prime factor list. |
| Replace 15 with the quotient from dividing 15 by the prime number 3: |
| 15 ÷ 3 = 5 |
| Can the prime number 3 be divided into 5 without leaving a remainder? |
| No, 5 divided by 3 leaves a remainder of 2. |
| Increment the prime number 3 to find the next prime number: 3 + 1 = 4 |
| Is 4 a prime number? |
| No, 4 is not a prime number. |
| Increment the prime number 4 to find the next prime number: 4 + 1 = 5 |
| Is 5 a prime number? |
| Yes, 5 is a prime number. |
| As the prime number 5 matches the number 5 add this to the prime factor list and you can now stop as you have all the possible prime factors for 120. |
| Therefore, the prime factors of 120 are 2, 2, 2, 3 and 5. |
| To check your answer multiply all the numbers together in the prime factor list and this should match your original number. |
| 2 × 2 × 2 × 3 × 5 = 120 |
As you can see from the above steps finding the prime factors of a number is finding all the prime numbers that can be divided into the original number.
Summary
Finding the prime factors of a number involves knowing what a prime number is and then incrementing through each prime number to determine if it is a factor of the original number. If the prime number can be divided into the original number reduce the original number by the prime factor and see if the same prime number is a factor of the new quotient.
If not progress to the next prime number and repeat the process of checking if the new prime number is a factor of the quotient.
To progress quicker through this process memorize the first handful of prime numbers (maybe all the prime numbers up to 20) and this will spare you needing to ask if a number is prime as you increment to the next prime number as you will just know what the next prime number will be.
At the end of it all you will have a list of prime numbers and this will be your prime factor list.
The prime factors of 120 are 2, 2, 2, 3 and 5.
To check your answer simply multiply each of the numbers in your factor list to see if you get the original number.