What is a Factor?

A factor is a number that is multiplied in order to get another number.

Examples:

2 and 5 are factors of 10, because 2 x 5 = 10.

1 and 10 are also factors of 10, because 1 x 10 = 10

Thus, the factors of 10 are 1, 2, 5, and 10.


Note:

Take note that a number has many factors.


HOW TO FIND THE FACTORS OF A NUMBER?


There are two ways to determine the factors of a particular number.

Division


In this method, the number is divided by a chosen number. If the remainder is 0, then it is a factor.


This method is used to determine if a certain number is a factor of another number.


Example


Example 1:
 Yes

Explanation :

`3`
___
` 5 ) 15`
`- 15`
_____
`0`

Since the remainder is 0, therefore 5 is a factor of 15.

Example 2:
 No

Explanation :

`3`
___
` 3 ) 10`
`- 9`
_____
`1`

Since the remainder is not 0, therefore 3 is a not factor of 10.

Example 3:
 Yes

Explanation :

`4`
___
` 4 ) 16`
`- 16`
_____
`0`

Since the remainder is 0, therefore 4 is a factor of 16.


Factor Tree


A factor tree is a diagram to find the factors of a number. In this process, we first find the two numbers whose multiplication will gives us the given number (so for a given number 12 - we get 2 other number - 3 and 4 whose multiplication will give 12)

Now in next step, we use above approach to get the factors of 3 and 4 and write them in tree diagram and will repeat the process of factoring until no factor of any of these two number are possible.

This method is used to determine all possible factors of a number.

Example


Example 1:

Explanation :

24 = 2 x 2 x 2 x 3.
therefore 2 and 3 are factors of 24

other factors of 24 are

2 x 2 = 4
2 x 2 x 2 = 8
2 x 3 =6
2 x 2 x 3 =12

Example 2:

Explanation :

30 = 2 x 3 x 5.
therefore 2 , 3 and 5 are factors of 30

other factors of 30 are

2 x 3 = 6
3 x 5 = 15
2 x 5 =10

Example 3:

Explanation :

30 = 2 x 2 x 3 x 3.
therefore 2 and 3 are factors of 36

other factors of 30 are

2 x 2 = 4
3 x 3 = 9
2 x 3 x 3 =18
2 x 3 = 6
2 x 2 x 3 = 12

Example 4:

Explanation :

48 = 2 x 2 x 2 x 2 x 3.
therefore 2 and 3 are factors of 48

other factors of 48 are

2 x 2 = 4
2 x 2 x 2 = 8
2 x 2 x 2 x 2 = 16
2 x 3 =6
2 x 2 x 3 = 12
2 x 2 x 2 x 3 24

Example 5:

Explanation :

72 = 2 x 2 x 2 x 3 x 3.
therefore 2 and 3 are factors of 72

other factors of 72 are

2 x 2 = 4
2 x 2 x 2 = 8
2 x 3 = 6
2 x 2 x 3 =12
2 x 2 x 2 x 3 = 24
2 x 2 x 3 x 3 = 36

Example 6:

Explanation :

60 = 2 x 2 x 5 x 3.
therefore 2,3 and 5 are factors of 60

other factors of 60 are

2 x 2 = 4
2 x 5 = 10
2 x 3 = 6
3 x 5=15
2 x 2 x 5 =20
2 x 2 x 3 = 12
2 x 5 x 3 = 30

Example 7:

Explanation :

45 = 3 x 3 x 5.
therefore 3 and 5 are factors of 45

other factors of 45 are

3 x 3 = 9
3 x 5 = 15

Example 8:

Explanation :

28 = 2 x 2 x 7.
therefore 2 and 7 are factors of 28

other factors of 28 are

2 x 2 = 4
2 x 7 = 14

Example 9:

Explanation :

18 = 2 x 3 x 3.
therefore 2 and 3 are factors of 18

other factors of 18 are

2 x 3 = 6
3 x 3 = 9

Example 10:

Explanation :

32 = 2 x 2 x 2 x 2 x 2.
therefore 2 are factor of 32

other factors of 32 are

2 x 2 = 4
2 x 2 x 2 = 8
2 x 2 x 2 x 2 = 16

Example 11:

Explanation :

12 = 2 x 2 x 3.
therefore 2 and 3 are factors of 12

other factors of 12 are

2 x 2 = 4
2 x 3 = 6

Example 12:

Explanation :

40 = 2 x 2 x 2 x 5.
therefore 2 and 5 are factors of 40

other factors of 40 are

2 x 2 = 4
2 x 2 x 2 = 8
2 x 5 =10

Example 13:

Explanation :

54 = 2 x 3 x 3 x 3.
therefore 2 and 3 are factors of 54

other factors of 12 are

2 x 3 = 4
3 x 3 = 9
3 x 3 x 3 = 27

Example 14:

Explanation :

56 = 2 x 2 x 2 x 7.
therefore 2 and 7 are factors of 56

other factors of 56 are

2 x 2 = 4
2 x 2 x 2 = 8
2 x 7 = 14
2 x 2 x 7 =28

Example 15:

Explanation :

75 = 3 x 5 x 5.
therefore 3 and 5 are factors of 75

other factors of 75 are

3 x 5 = 15
5 x 5 = 25


WHAT IS A PRIME NUMBER?


Prime number is a number whose factors are itself and 1.

Examples: 2, 3, 5, 7, 9, 11

*2 is the only even number that is a prime number.


WHAT IS A PRIME FACTORIZATION?


Prime factorization is the process of determining the prime factors to be multiplied together resulting to the original number.


Factor tree is recommended for prime factorization.


Example 1:

Explanation :

50

10
5

2
5
The prime factorization of 50 is 2 x 5 x 5.

Example 2:

Explanation :

81

9
9

3
3
3
3
The prime factorization of 81 is 3 x 3 x 3 x 3.

Example 3:

Explanation :

42

6
7

3
2
The prime factorization of 81 is 2 x 3 x 7.

Example 4:

Explanation :

63

9
7

3
3
The prime factorization of 63 is 3 x 3 x 7.

Example 5:

Explanation :

75

25
3

5
5
The prime factorization of 75 is 5 x 5 x 3.

Example 6:

Explanation :

48

24
2

12
2

6
2

3
2 The prime factorization of 63 is 3 x 2 x 2 x 2 x 2.






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