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.
Take note that a number has many factors.
There are two ways to determine the factors of a particular number.
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.
`3`
___
` 5 ) 15`
`- 15`
_____
`0`
Since the remainder is 0, therefore 5 is a factor of 15.
`3`
___
` 3 ) 10`
`- 9`
_____
`1`
Since the remainder is not 0, therefore 3 is a not factor of 10.
`4`
___
` 4 ) 16`
`- 16`
_____
`0`
Since the remainder is 0, therefore 4 is a factor of 16.
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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.
50
10
5
2
5
The prime factorization of 50 is 2 x 5 x 5.
81
9
9
3
3
3
3
The prime factorization of 81 is 3 x 3 x 3 x 3.
42
6
7
3
2
The prime factorization of 81 is 2 x 3 x 7.
63
9
7
3
3
The prime factorization of 63 is 3 x 3 x 7.
75
25
3
5
5
The prime factorization of 75 is 5 x 5 x 3.
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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