The process of finding the factors of a number is called as factoring a number.

The positive integers which are dividing the number exactly are called as factors of a number. Numbers that are divided by 1 and itself is called as prime numbers.

Some of the prime numbers are 2, 3, 5, 7, 9, 11, and 13.

Factors could be numerical or literal. Numerical factors are numbers used as factors whereas, literal factors are alphabets or letters used to represent the numbers being multiplied.

Interchanging the factors does not alter the result and it is done to check the product, to simplify or just to re-arrange the factors in a preferred order.

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**Factor** is defined as a number that divides exactly into another number. In the example shown below, we can see the steps for factoring numbers.

**Example:**

Find the factors of 58.

**Solution:**

58 is divided by 1, 2, 29 and 58

So, 1, 2, 29 and 58 are the factors of the given number 58

**Answer:**

1, 2, 29 and 58

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Factoring large numbers take time to compute. And so, there are some easy ways to find few factors of such numbers.

Some of them are as follows.

- Even number contains a factor of 2.
- Number which is ending in 5 has a factor of 5.
- Number which ends with 0 contain the factors of 2 and 5.

Given below are some of the examples in factoring numbers.

48 can be divided by 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

So, 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 are the factors of the given number 48.

Multiples of the given numbers is 2 x 2 x 2 x 2 x 3

Answer:

1, 2, 3, 4, 6, 8, 12, 16, 24 and 48

Prime factors of 48:

2 x 2 x 2 x 2 x 3

87 can be divided by 1, 3, 29 and 87.

So, 1, 3, 29 and 87 are the factors of the given number 87

Multiples of the given numbers is 3 x 29

Factors of 87 are 1, 3, 29 and 87

Prime factors of 87 are 3 x 29

126 can be divided by 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126.

So, 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126 are the factors of the given number 126.

Multiples of the given numbers is 2 x 3 x 3 x 7

Factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63 and 126

Prime factors of 126 are 2 x 3 x 3 x 7

Factoring prime numbers of 36 is given by as follows,

36 divided by 2 = 18

18 divided by 2 = 9

9 divided by 3 = 3

3 divided by 3 = 1

So, the prime factors of 36 are 2, 2, 3, 3.

Prime factors of 63 is given by,

63 divided by 3 = 21

21 divided by 3 = 7

7 divided by 7 = 1

The prime factors of 63 = 3 x 3 x 7

Prime factors of 336 is given by,

336 divided by 2 = 168

168 divided by 2 = 84

84 divided by 2 = 42

42 divided by 2 = 21

21 divided by 3 = 7

7 divided by 7 = 1

The prime factors of 336 = 2 x 2 x 2 x 2 x 3 x 7

More topics in Factoring a Number | |

Factoring Expressions | Factoring |

Factoring Quadratic | |

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