How to Find Factors of a Number?
We can find all the factors of a given number in the following two ways:
- Multiplication method
- Division Method
- Factor Tree Method
Finding Factors Using Multiplication Method
In this method, we have to find all the pairs of whole numbers whose product is equal to the given number. Let us consider an example to understand that better.
Example: Find all the factors of 24 using the multiplication method.
Solution:
We have to find all the pairs of whole numbers whose product is 12, like
- 1 × 24 = 24
- 2 × 12 = 24
- 3 × 8 = 24
- 4 × 6 = 24
Here the product of the following pairs is 24.
(1, 24) , (2, 12), (3, 8) and (4, 6)
Hence, all these numbers 1, 2, 3, 4, 6, 8, 12 and 24 are factors of 24.
Finding Factors Using Division Method
In this method, we have to find all the divisors of the given number which are exactly divisible by it. Here we start dividing the given number by 1 and continue dividing it by the next number until we reach the square root of that number (or until we reach the number itself).
If the number exactly divides the original number then it is a factor else not. Let us consider an example to understand that better.
Example: Find all the factors of 12 using the division method.
Solution:
We will take every natural number less than 12 and will check whether it is divisible by 12 or not
- 12 ÷ 1 = 12 (remainder = 0)
- 12 ÷ 2 = 6 (remainder = 0)
- 12 ÷ 3 = 4 (remainder = 0)
- 12 ÷ 4 = 3 (remainder = 0)
- 12 ÷ 5 = 2 (remainder = 2)
- 12 ÷ 6 = 2 (remainder = 0)
- 12 ÷ 7 = 1 (remainder = 5)
- 12 ÷ 8 = 1 (remainder = 4)
- 12 ÷ 9 = 1 (remainder = 3)
- 12 ÷ 10 = 1 (remainder = 2)
- 12 ÷ 11 = 1 (remainder = 1)
- 12 ÷ 12 = 1(remainder = 0)
So, the numbers that are exactly divides 12 are 1, 2, 3, 4, 6, and 12. Hence these numbers are the factors of 12.
Prime Factorization by Factor Tree Method
A factor tree is a diagrammatic representation of the prime factors of a number. In this method, we find the factors of a number and then further factorize them until we get all the factors as prime numbers. Here, we consider the given number as the top of a tree and all its factors as its branches.
To find the prime factorization by factor tree method, we follow the below given steps:
- First, split the given number (which is placed at the top of the tree) into factors.
- Then write down the factor pair as the branches of the tree.
- Again split the composite factors obtained in step 2.
- Repeat steps 2 and 3 until all the factors become prime numbers.
- Lastly, multiply all the prime factors obtained.
Factors of a Number
Factors of a Number: In mathematics, a factor is a number that divides another number perfectly, leaving no remainder. Factors can also be seen as pairs of numbers that, when multiplied together, result in the original number. For example, 2 and 3 are factors of 6 because multiplying them together gives 6. A single number can have multiple factors.
Let’s learn about the factors of prime and composite numbers, common factors, and methods to find them.
Table of Content
- What are Factors of a Number?
- Factors of a Number Definition
- Factors of a Number Properties
- How to Find Factors of a Number?
- Finding Factors Using Multiplication Method
- Finding Factors Using Division Method
- Prime Factorization by Factor Tree Method
- How To Check whether a Number is a Factor?
- Factors of Prime Numbers
- Factors of Composite Numbers
- Factors of Square Numbers
- Common Factors
- Prime Factors of a Number
- Factors Formulas
- Sum of Factors
- Number of Factors
- Product of Factors
- Factors and Multiples
- Difference between Factors and Multiples
- Solved Examples on Factors of Numbers
- Practice Questions on Factors of Number