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How Do I find Prime Factors?

prime factorisation on the calculator example of 130 = 2 x 5 x 13

What are prime factors?

We know that factors are the numbers that divide perfectly into another number without a remainder. So, prime factors are all the prime numbers that divide perfectly into our number without a remainder.

Example: Find the prime factors of 130

Steps:

  1. Let’s start by thinking about the first 5 prime numbers. These are 2, 3, 5, 7, and 11.
  2. Now we try to divide our number by the first prime number., e.g. 130 ÷ 2 = 65. We write down 2 as a prime factor.
  3. If our number is divisible by the prime number, then we repeat step 2, with the answer we got, e.g. 65 ÷ 2 = 32,5, so 2 is not another prime factor, and we try 3. e.g. 65 ÷ 3 = 21.6666… So 3 is not a prime factor and we try 5. 65 ÷ 5 = 13. We write down 5 as the next prime factor.
  4. We can see that 13 is a prime number, so we have found all our prime factors ⇒ 130 = 2 x 5 x 13.

 

Let’s do another example: Find the prime factors of 64. 

  1. 64 ÷ 2 = 32
  2. then 32 ÷ 2 = 16
  3. then 16 ÷ 2 = 8
  4. and 8 ÷ 2 = 4
  5. and 4 ÷ 2 = 2
  6. and finally 2 ÷ 2 = 1
  7. So our prime factors are ⇒ 64 = 2 x 2 x 2 x 2 x 2 x 2 or 26

Let’s do one more example: Find the prime factors of 300. 

  1. 300 ÷ 2 = 150
  2. 150 ÷ 2 = 75  (we can see that the number is not even so we will try 3 next)
  3. 75 ÷ 3 = 25
  4. 25 ÷ 5 = 5
  5. 5 ÷ 5 = 1
  6. So our prime factors are ⇒ 300 = 2 x 2 x 3 x 5 x 5 or 22 x 3 x 5

 

If we want to check our answers on the calculator we can follow these steps:

  1. Type in your number, e.g. 130
  2. Press   
  3. Then press   
  4. You should see:

prime factorisation on the calculator example of 130 = 2 x 5 x 13

 

 

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