To find the prime factorization of a number:
Begin by listing 2 numbers that will multiply to make your number.
6 = 2 * 3
Can we find 2 numbers to multiply to make 2, or 3? (aside from 1)
No, of course not.
In fact, 2 and 3 are prime. Once you have all primes, you can stop.
6 = 2 * 3
2 * 3 is the prime factorization of 6.
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6 is not a prime number but it is a factor of 72
It is a factor of 132, not a prime factor.
Both 6 and 9 have the number 3 as a prime factor. 6 = 3 x 2 9 = 3 x 3
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.
All numbers have factors. Some factors are prime numbers. These are known as prime factors. 2 and 3 are prime factors of 6. 1 and 6 are not prime factors of 6.