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Rule 9: Factoring Integers

**To factor an integer, simply break the integer down into a group of
numbers whose product equals the original number. Factors are
separated by multiplication signs. Note that the number 1 is the
factor of every number. All factors of a number can be divided evenly
into that number.**

**Example 1:** Factor the number 3.

**Answer:**

- Since 3 x 1 = 3, the factors of 3 are 3 and 1.

**Example 2:** Factor the number 10.

**Answer:**

- Since 10 can be written as 5 x 2 x 1, the
factors of 10 are 10, 5, 2, and 1. The number 10 can be divided by
10, 5, 2, and 1.

**Example 3:** Factor the number 18.

**Answer:**

- The number 18 can be written as 18 x 1 or 9 x 2 or 6 x 3 or 3 x 3 x 2.
Since 18 can be divided by 18, 9, 6, 3, 2, and 1, then 18, 9, 6, 3, 2,
and 1 are factors of 18.

**Example 4:** Factor the number 24.

**Answer:**

- The number 24 can be written as 24 x 1 or 12 x 2 or 8 x 3 or 4
x 6 or 2 x 2 x 2 x 3. Since 24 can be divided by 24, 12, 8, 6, 4, 3, 2, and
1, then 24, 12, 8, 6, 4, 3, 2, and 1 are factors of 24.

**Example 5:** Factor the number 105.

**Answer:**

- The number 105 can be
written as 105 x 1 or 21 x 5 or 3 x 7 x 5 or 15 x 7 or 35 x 3. Since 105 can be divided
by 105, 35, 21, 15, 7, 5, 3, and 1, then 105, 35, 21, 15, 7, 5, 3, and 1 are factors
of 105.

**Example 6:** Factor the number 1200 completely.

**Answer:**

- This instruction means to factor 1200 into a
set of prime factors (factors that cannot again be factored). The number 1200 can
be written as 1200 x 1 or 100 x 12. Note the 100 can again be
factored to 10 x 10 and the 12 can be factored to 6 x 2. So now you
have 1200 = 100 x 12 = 10 x 10 x 6 x 2. This factored set can again
be factored to (2 x 5) x (2 x 5) x (2 x 3) x 2 x 1. The number 1200
is factored completely as 5 x 5 x 3 x 2 x 2 x 2 x 2 x 1.

**Work the following problems and click on Answer to check your
results.**

Problem 1: Factor 15 completely.

**Answer**

**Problem 2:** Factor 300 completely.

**Answer**

**Problem 3:** Factor 4000 completely.

**Answer**

**Problem 4:** Factor -3 completely.

**Answer**

**Problem 5:** Is 3 a factor of 10? Why?

**Answer**

**Problem 6:** Is 7 a factor of 21? Why?

**Answer**

**Problem 7:** Is 4 a factor of 87? Why?

**Answer**

Menu Back to Simple Fractions

[Identification]
[Reducing Fractions]
[Multiplication]
[Division]
[Building Fractions]
[Addition]
[Subtraction]
[Order of Operation]

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Author: Nancy
Marcus

Fri Aug 30 17:09:13 MDT 1996

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