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Factors

A factor of a number divides the number. For example, 2, 3, and 4 are all factors of 12. Similarly, we say that 12 is a multiple of 2, or a multiple of 3, because one can multiply 2 by a whole number to get 12. A number is a multiple of its factors. To determine whether a number is a factor of another number, we generally use the divisibility rules discussed last section.

Primes

A prime number is a number divisible by only 1 and itself (the number 1 itself is not considered prime). For example, 17 is prime because it is divisible by only 1 and 17. The first few primes, in increasing order, are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ...

To determine whether a number is prime, it is not necessary to check whether it is divisible by every number less than itself. It is only necessary to check whether it is divisible by any prime up to half its value. One might do the following computations to check whether 91 is prime:

  1. Is 91 divisible by 2? No, it does not end with an even number.
  2. Is 91 divisible by 3? No, 9 + 1 = 10, which is not divisible by 3.
  3. Is 91 divisible by 5? No, 91 does not end with 0 or 5.
  4. Is 91 divisible by 7? Yes! 91/7 = 13.
Therefore, 91 is not prime.

Composites

A composite number is a number that has at least one factor besides 1 and itself, or any number which is not prime (although the number 1 is neither prime nor composite). For example, 91 is a composite number. To determine whether a number is composite, determine whether or not it is prime. If it is prime, it is not composite; if it is not prime, then it is composite.

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