Factors are numbers we can multiply together to get a number.
A multiple is the product of a number and any whole number except zero.
To find the factors of a number, we can follow the below steps
Step 1 :
Use multiplication or division facts to find factors. Start with 1 x the given number. Every counting number has at least two factor 1 and the number itself. So, 1 and 8 are factors of 8.
Step 2 :
Test other factor pairs. The only possible whole number factors of 8 are numbers from 1 to 8.
Step 3 :
Continue until the factors repeat
Note :
A factor always divides the product without a remainder.
Example 1 :
Find the factors of 45.
Solution :
Factors of 45 are 1, 3, 5, 9, 15, 45.
Example 2 :
Write the factors of 15.
Solution :
15 = 1 x 15
15 = 5 x 3
Factors of 15 are 1, 3,5 and 15.
Example 3 :
Write the factors of 18.
Solution :
18 = 1 x 18
18 = 2 x 9
18 = 3 x 6
Factors of 18 are 1, 2, 3, 6, 9 and 18.
Example 4 :
List the first 5 multiples of 8.
Solution :
To get the first 5 multiple of 8, we need to multiply 8 by 1, 2, 3, 4 and 5 respectively.
1 x 8 = 8
2 x 8 = 16
3 x 8 = 24
4 x 8 = 32
5 x 8 = 40
First 5 multiples of 8 are 8, 16, 24, 32 and 40.
If the given number is small, it is easy to find number of factors. But, for larger numbers, we can't just count one by one. This is a nice trick to find how many factors are in an integer.
To find the number of factors of an integer, we need to follow the steps given below.
Step 1 :
Split the given number as prime factors using prime factorization method or tree method.
Step 2 :
Take all exponents and add one to each of them.
Step 3 :
Multiply the modified exponents together.
Let us see an example to understand the above method
Example 5 :
Find the number of factors of 48
Solution :
To get the number of factors of 48, first we have to find the factors.
48 = 1 x 48
48 = 2 x 24
48 = 3 x 16
48 = 4 x 12
48 = 6 x 8
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.
Number of factors of 48 = 10
We can get the same answer in the below method too.
Step 1 :
For that, first we have to split the given number 48 as prime factors using prime factorization method.
Step 2 :
48 = 2⁴ x 3¹
Take all exponents and add one to each of them. So, we get 2⁵ x 3²
Step 3 :
Multiplying the modified exponents, we get 5 x 2 = 10.
Hence, the number of factors of 48 is 10.
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