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### Multiples and Factors

```Date: 06/02/2003 at 19:39:45
From: Sarah
Subject: Multiples and Factors

What is the difference between multiples and factors?
```

```
Date: 06/03/2003 at 10:35:23
From: Doctor Sarah
Subject: Re: Multiples and Factors

Hi Sarah - thanks for writing to Dr. Math.

MULTIPLES
Multiples of a number are the result of multiplying that number by
another whole number.

You can see multiples of numbers in a multiplication table.  For
example, the first multiples of 6 from 6 to 72 are:

x | 2   3   4   5   6   7   8   9  10  11  12
--+------------------------------------------
6 |12  18  24  30  36  42  48  54  60  66  72

FACTORS
A factor of a number will divide that number evenly, without any
remainder. For example, 2 is a factor of 12 because 12/2 = exactly 6.
And 6 is a factor of 12 because 12/6 = exactly 2.

Notice that 12 has other factors: it is evenly divisible by both 3 and
4, and by 1 and itself (all numbers are evenly divisible by 1 and
themselves; if they have no other factors, they are called "prime
numbers"). So the factors of 12 (the numbers that divide it evenly)
are

1, 2, 3, 4, 6, 12

For lots more about prime factorization, see:

Prime Factoring
http://mathforum.org/library/drmath/sets/select/
dm_prime_factors.html

- Doctor Sarah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication
Middle School Factoring Numbers

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