How to Factor Numbers? (+FREE Worksheet!)

Factoring, in mathematics, refers to the simplification or reduction of a number, a polynomial, etc., to a result that can not be further reduced or simplified. In this post, you can learn how to factor numbers easily.

“Factors” are the numbers we multiply to get another number. Factoring, in mathematics, refers to the simplification or reduction of a number, a polynomial, etc., to a result that can not be further reduced or simplified. Known as factorization, this method is primarily used in polynomial simplification. In this post learn how to factor numbers easily.

Step-by-step guide to factoring numbers

Factoring numbers means breaking the numbers into their prime factors.
A set of prime numbers is a subset of natural numbers in which each of its members has only two positive divisors, one of which is \(1\) and the other is the number itself.
First few prime numbers: \(2, 3, 5, 7, 11, 13, 17, 19\)

Some conditions for divisibility of natural numbers by prime numbers

Divisibility by 2: The necessary condition for a number to be divisible by \(2\) is that its unit number is even.

Divisibility by 3: The necessary condition for a number to be divisible by \(3\) is that the sum of the digits of that number is divisible by \(3\).

Divisibility by 5: The condition for a number to be divisible by \(5\) is that its unit digit is zero or \(5\).

Divisibility by 11: A number is divisible by \(11\) if the difference between the sum of even-order digits (units, hundreds, tens of thousands, etc.) and the sum of odd-numbered digits (tens, thousands, hundreds, etc.) is divisible by \(11\).

To factor a number, start with the smallest prime number which is \(2\). Is the number divisible by \(2\)? If so, divide it by \(2\) and do the same for the result. If not, check the next prime number which is \(3\), and do the same process.

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Factoring Numbers – Example 1:

List all positive factors of \(8\).

Solution:

Write the upside-down division: \(8\) is divisible by \(2\). Then:

8	2
4	2
2	2
1

The first column shows all the factors of number \(8\).
Then: \(8=2 \ \times \ 2 \ \times \ 2\) or \(8=2^{3}\)

All factors of \(8\) are: \(1, 2, 4, 8\)

Factoring Numbers – Example 2:

List all positive factors of \(24\).

Solution:

Write the upside-down division:

24	2
12	2
6	2
3	3
1

The second column is the answer.
Then: \(24= 2 \ \times \ 2 \ \times \ 2 \ \times \ 3\)
or \(24=2^{3} \ \times \ 3\)

All factors of \(24\) are: \(1, 2, 3, 4, 6, 8, 12\) and \(24\)

Factoring Numbers – Example 3:

List all positive factors of \(12\).

Solution:

Write the upside-down division:

12	2
6	2
3	3
1

The second column is the answer.
Then: \(12=2×2×3\)
or \(12=2^2×3\)

All factors of \(12\) are: \(1, 2, 3, 4, 6, 12\)

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Factoring Numbers – Example 4:

List all positive factors of \(20\).

Solution:

Write the upside-down division:

20	2
10	2
5	5
1

The second column is the answer.
Then: \(20=2×2×5\) or \(20=2^2×5\)

All factors of \(20\) are: \(1, 2, 4, 5, 10\) and \(20\)

Exercises for Factoring Numbers

List all positive factors of each number.

\(\color{blue}{68}\)
\(\color{blue}{56}\)
\(\color{blue}{24}\)
\(\color{blue}{40}\)
\(\color{blue}{86}\)
\(\color{blue}{78}\)

Download Factoring Numbers Worksheet

\(\color{blue}{1, 2, 4, 17, 34, 68}\)
\(\color{blue}{1, 2, 4, 7, 8, 14, 28, 56}\)
\(\color{blue}{1, 2, 3, 4, 6, 8, 12, 24}\)
\(\color{blue}{1, 2, 4, 5, 8, 10, 20, 40}\)
\(\color{blue}{ 1, 2, 43, 86 }\)
\(\color{blue}{ 1, 2, 3, 6, 13, 26, 39, 78 }\)

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Step-by-step guide to factoring numbers