fators and factorization

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FACTORS and Prime Factorization

The factors of a number are those numbers that divide evenly into it. We talk about this using the counting numbers. For instance, the factors of 10 are 1,2,5,and 10. We know that multiplying 20 by 0.5 we could get 10 but we do not count those as factors.

A prime number has exactly two factors, 1 and itself. Some examples are 3,5, and 7. Composite numbers have more than two factors. Some examples are 4,6, and 8.
1 is always a factor. Multiplying by 1 does not change the value of a number. We refer to 1 as the identity for multiplication.
0 and 1 are not considered prime. 1 has only itself as a factor and 0 has any number as a factor.

A number can be expressed by its prime factorization. That means thinking of more than factor pairs e.g. 12 can be seen as 2 * 6 or alternatively as 2 * 2 * 3 when 6 is expressed with prime factors. Basically that means breaking down factors until only primes remain. The prime factorization of a number is unique.

120 = 8 * 15 = 2 * 2 * 2 * 3 * 5

this is the prime factorization of 120 and can be written as 2³* 3 * 5

75 = 3 * 25 = 3 * 5 * 5

this is the prime factorization and can be written as 3 * 5²