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A factor of a composite number need not be a Prime number, some factors are themselves composite. Prime factorisation is continuing to factorise each factor unless it is a prime.

For example, start with 30.

6 goes into 30 so finding a factor is satisfied by simply identifying 6 as a factor of 30.

Now 30 = 5*6 where 5 is a prime, but 6 is not so we need to factorise 6.

6 = 2*3

and therefore, 30 = 5*2*3 = 2*3*5

The last is the prime factorisation of 30.

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Q: What is the difference between prime factorization and finding a factor?
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