A factor of an integer n, also known as a divisor of n is an integer m that when multiplied by another integer produces n. This can also be worded that n is a multiple of m. An integer n is (evenly) divisible by another integer m if m is a divisor of n. This means that dividing n by m results in no remainder.
A multiple is the product of any quantity of an integer. For example, 35 is a multiple of 7 because 35 = 7 * 5.
There are many ways one can describe the relationship between factors, divisors and multiples. For example, the following three statements are the same:
- n/m is an integer
- m divides n
- m is a factor of n
Example: What are the factors of 8?
- 1, 2, 4, 8
Is this all? No. We must remember the negative factors as well.
- -8, -4, -2, -1
For a total of 8 factors:
- -8, -4, -2, -1, 1, 2, 4, 8
Knowing that we have both negative and positive factors, it is important to remember that the minimum number of factors a number can have is 2!
Example: What are the factors of 1?
- -1, 1
Example: How many multiples does the number 7 have?
- An infinite amount
Example: What are the first 5 multiples of 9?
- 9, 18, 27, 36, 45