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Factoring a Number


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

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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.

How to Factor Numbers

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Given below are some of the examples in factoring numbers.

Solved Examples

Question 1: Determine the factors and multiples factors and multiples of the number 48
Solution:
 
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.

Prime factor:

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
 

Question 2: Determine the factors and multiples of the number 87.
Solution:
 
87 can be divided by 1, 3, 29 and 87.

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

Prime factor:

Multiples of the given numbers is 3 x 29

Answer:

Factors of 87 are 1, 3, 29 and 87

Prime factors of 87 are 3 x 29
 

Question 3: Determine the factors and multiples of the number 126
Solution:
 
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.

Prime factor:

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

Answer:

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

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Factoring prime numbers of any number can be found by dividing the number by lowest prime number, say 2 until remainder 0. If occurs any remainder, then divide by next prime number.

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.

Solved Examples

Question 1: Find the prime factors by factoring 63
Solution:
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


Question 2: Find the prime factors by factoring 336.
Solution:
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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