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If you know the prime factorization of a number, you can find out the total number of factors.
Example: 210
21 x 31 x 51 x 71 = 210
Add one to the exponents and multiply them.
2 x 2 x 2 x 2 = 16, the total number of factors.
You know that 1, 2, 3, 5, and 7 are factors. You need three more to get halfway.
2 x 3 = 6
2 x 5 = 10
2 x 7 = 14
Divide all those numbers into 210.
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
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Do you need to know all of the factors of a number to know it is prime or composite?
To know that a number is prime you need to know that it has no factors other than 1 and the number itself.To know that a number is composite you only need to know one factor other than the number itself or 1.
Why do you need to know all of the factors to a number to know if it is a prime or composite number?
You don't.If you know just one factor, other than 1 and the number itself, you will know that the number is composite.A prime has only two factors: 1 and itself. So all the factors is no big deal.
How do you know a number is a composite number?
It has more than two factors.
How many factors does aprime number have?
Two factors
How many number factors does 50 have?
Six factors.
