103 LearnersLast updated on May 26th, 2025
Factors of 468
Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 468, how they are used in real life, and tips to learn them quickly.
What are the Factors of 468?
The numbers that divide 468 evenly are known as factors of 468. A factor of 468 is a number that divides the number without a remainder.
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, and 468.
Negative factors of 468: -1, -2, -3, -4, -6, -9, -12, -13, -18, -26, -36, -39, -52, -78, -117, -156, -234, and -468.
Prime factors of 468: 2, 3, and 13.
Prime factorization of 468: 2² × 3² × 13.
The sum of factors of 468: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 13 + 18 + 26 + 36 + 39 + 52 + 78 + 117 + 156 + 234 + 468 = 1188
How to Find Factors of 468?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the division method
- Prime factors and prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 468. Identifying the numbers which are multiplied to get the number 468 is the multiplication method.
Step 1: Multiply 468 by 1, 468 × 1 = 468.
Step 2: Check for other numbers that give 468 after multiplying
2 × 234 = 468
3 × 156 = 468
4 × 117 = 468
6 × 78 = 468
9 × 52 = 468
12 × 39 = 468
13 × 36 = 468
18 × 26 = 468
Therefore, the positive factor pairs of 468 are: (1, 468), (2, 234), (3, 156), (4, 117), (6, 78), (9, 52), (12, 39), (13, 36), (18, 26).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 468 by 1, 468 ÷ 1 = 468.
Step 2: Continue dividing 468 by the numbers until the remainder becomes 0.
468 ÷ 1 = 468
468 ÷ 2 = 234
468 ÷ 3 = 156
468 ÷ 4 = 117
468 ÷ 6 = 78
468 ÷ 9 = 52
468 ÷ 12 = 39
468 ÷ 13 = 36
468 ÷ 18 = 26
Therefore, the factors of 468 are: 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468.
Prime Factors and Prime Factorization
The factors can be found by dividing them with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using a factor tree
Using Prime Factorization: In this process, prime factors of 468 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
468 ÷ 2 = 234
234 ÷ 2 = 117
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
The prime factors of 468 are 2, 3, and 13. The prime factorization of 468 is: 2² × 3² × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 468 is divided by 2 to get 234.
Step 2: Now divide 234 by 2 to get 117.
Step 3: Then divide 117 by 3 to get 39.
Step 4: Divide 39 by 3 to get 13.
Here, 13 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 468 is: 2² × 3² × 13.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.
Positive factor pairs of 468: (1, 468), (2, 234), (3, 156), (4, 117), (6, 78), (9, 52), (12, 39), (13, 36), and (18, 26).
Negative factor pairs of 468: (-1, -468), (-2, -234), (-3, -156), (-4, -117), (-6, -78), (-9, -52), (-12, -39), (-13, -36), and (-18, -26).
Common Mistakes and How to Avoid Them in Factors of 468
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 468, 1 and 468 are also factors.
Factors of 468 Examples
Problem 1
There are 13 teams and 468 apples. How will they divide the apples equally?
They will get 36 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of teams.
468/13 = 36
Problem 2
A garden is rectangular, the width of the garden is 18 meters, and the total area is 468 square meters. Find the length?
26 meters.
Explanation
To find the length of the garden, we use the formula,
Area = length × width
468 = length × 18
To find the value of the length, we need to shift 18 to the left side.
468/18 = length
Length = 26.
Problem 3
There are 6 boxes and 468 chocolates. How many chocolates will be in each box?
Each box will have 78 chocolates.
Explanation
To find the chocolates in each box, divide the total chocolates by the boxes.
468/6 = 78
Problem 4
In a seminar, there are 468 participants, and 12 groups. How many participants are there in each group?
There are 39 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
468/12 = 39
Problem 5
468 books need to be arranged in 4 shelves. How many books will go on each shelf?
Each of the shelves has 117 books.
Explanation
Divide total books by shelves.
468/4 = 117
FAQs on Factors of 468
1.What are the factors of 468?
2.Mention the prime factors of 468.
3.Is 468 a multiple of 9?
4.Mention the factor pairs of 468?
5.What is the square of 468?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 468?
7.What are some fun ways kids in United Kingdom can practice Factors of 468 with numbers?
8.What role do numbers and Factors of 468 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 468 skills?
Important Glossaries for Factor of 468
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 468 are 1, 2, 3, 4, 6, 9,12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, and 468.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 13 are prime factors of 468.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 468 are (1, 468), (2, 234), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 468 is 2² × 3² × 13.
- Negative factors: Factors that are negative integers. For example, the negative factors of 468 are -1, -2, -3, etc.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
