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### Factors and Multiples

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Date: 01/27/98 at 15:36:25
From: SeasndExec
Subject: Factors and multiples

Dear Dr. Math,

My son is in 4th grade and he needs help with factors and multiples.
He must name the common multiple of pairs of numbers, for instance:
2 and 8, 3 and 6. It's been ages since I've done this and I don't want
to give him incorrect info.

Also, name the factors of each pair of numbers. What are the common
factors?

example: 6,8  5,15  etc.

Prime and composite numbers.

Very sincerely,
MHN
```

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Date: 01/27/98 at 16:38:07
From: Doctor Rob
Subject: Re: Factors and multiples

One way to do the first kind of problem is to write down a list of
multiples for each of the numbers, then find a number which appears
on both lists.

2, 4, 6, 8, 10, 12, ...
8, 16, 24, 32, 40, 48, ...
8 appears on both lists, so 8 is a common multiple.

3, 6, 9, 12, ...
6, 12, 18, 24, ...
6 and 12 appear on both lists, so they are common multiples of
3 and 6.

An analogous way to do the second kind of problem is to write down a
list of all the factors of each number, and look for numbers on both
lists:

6, 3, 2, 1
8, 4, 2, 1
2 and 1 appear on both lists, so are common factors.

5, 1
15, 5, 3, 1
5 and 1 appear on both lists, so are common factors.

A prime number is a whole number greater than 1 that can't be written
as a product of two other whole numbers greater than 1.  A composite
number is a whole number greater than 1 that can be written as a
product of two other numbers greater than 1.

Examples:

11 is prime

10 is composite, because 10 = 2*5, and 2 and 5 are prime

17143 is composite, because 17143 = 7*2449

7 is prime, but 2449 is composite, because 2449 = 31*79, and
31 and 79 are prime (thus 17143 = 7*31*79).

Think of a big multiplication table. Chop off the rows and columns
that deal with multiplication by 0 or 1. If the number appears in what
is left, it is composite, and if it doesn't appear there, it is prime.

Every whole number greater than 1 is either a prime number or can be
written as a product of two or more prime numbers. That is why prime
numbers are useful and important.

Telling whether a small number is prime or composite is not very hard,
but when the numbers get large, it is much more difficult.

-Doctor Rob,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Elementary Definitions
Elementary Number Sense/About Numbers
Elementary Prime Numbers
Middle School Definitions
Middle School Number Sense/About Numbers
Middle School Prime Numbers

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