FINDING FACTORS OF A NUMBER
About "Finding factors of a number"
Finding factors of a number :
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.
Question 1 :
Find the factors of 45
Solution :
Hence, factors of 45 are 1, 3, 5, 9, 15, 45.
Question 2 :
Write the factors of 15
Solution :
15 = 1 x 15
15 = 5 x 3
Hence, factors of 15 are 1, 3,5 and 15.
Question 3 :
Write the factors of 18
Solution :
18 = 1 x 18
18 = 2 x 9
18 = 3 x 6
Hence, factors of 18 are 1, 2, 3, 6, 9 and 18.
How to find how many factors are in a number?
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
Question 4 :
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.
Related Topics
- Generating equivalent numerical expressions
- Use repeated multiplication
- Division facts
- Exponents
- Using exponents
- Finding the value of a power
- Finding the value of each power
- Find the missing exponent
- Find the missing base
- Finding the factors of a number
- Finding the prime factorization of a number
- using ladder diagram for prime factorization
- Order of operations
- Exploring the order of operations
- Evaluating the numerical expression
- Using exponents with parentheses
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