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# Prime Factorisation

10

Prime Factors

Number

###### The process of showing a number as a product of primes is called **prime factorisation. **

###### Here are the steps to do it:

###### Start by dividing the number by the smallest prime number, which is 2. If the number is not divisible by 2, move to the next smallest prime number, which is 3. Repeat this process with each prime number until you reach a prime number that the number is divisible by.

###### Write down the prime factor you found in step 1 and the result of the division. Then, repeat step 1 with the result of the division until you reach a prime number.

###### Continue this process until the result of the division is 1. Write down the prime factors you found in each step.

###### The prime factorisation of the original number is the product of all the prime factors you found.

###### For example, let's find the prime factorisation of 120:

###### 120 is divisible by 2, so divide it by 2: 120 Ã· 2 = 60. Write down "2" and "60".

###### 60 is divisible by 2, so divide it by 2: 60 Ã· 2 = 30. Write down "2" and "30".

###### 30 is divisible by 2, so divide it by 2: 30 Ã· 2 = 15. Write down "2" and "15".

###### 15 is not divisible by 2, so divide it by 3: 15 Ã· 3 = 5. Write down "3" and "5".

###### 5 is a prime number. Write down "5" and "1".

###### (In the diagram, the primes have been circled)

###### The prime factorization of 120 is: 2 Ã— 2 Ã— 2 Ã— 3 Ã— 5 = 120.

###### Which can also be written as:

###### Let's try 96

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