137 LearnersLast updated on May 26th, 2025
Factors of 462
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 462, how they are used in real life, and tips to learn them quickly.
What are the Factors of 462?
The numbers that divide 462 evenly are known as factors of 462.
A factor of 462 is a number that divides the number without a remainder.
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, and 462.
Negative factors of 462: -1, -2, -3, -6, -7, -11, -14, -21, -22, -33, -42, -66, -77, -154, -231, and -462.
Prime factors of 462: 2, 3, 7, and 11.
Prime factorization of 462: 2 × 3 × 7 × 11.
The sum of factors of 462: 1 + 2 + 3 + 6 + 7 + 11 + 14 + 21 + 22 + 33 + 42 + 66 + 77 + 154 + 231 + 462 = 1160
How to Find Factors of 462?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using 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 462. Identifying the numbers which are multiplied to get the number 462 is the multiplication method.
Step 1: Multiply 462 by 1, 462 × 1 = 462.
Step 2: Check for other numbers that give 462 after multiplying:
2 × 231 = 462
3 × 154 = 462
6 × 77 = 462
7 × 66 = 462
11 × 42 = 462
14 × 33 = 462
21 × 22 = 462
Therefore, the positive factor pairs of 462 are: (1, 462), (2, 231), (3, 154), (6, 77), (7, 66), (11, 42), (14, 33), (21, 22).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result as whole numbers as factors. Factors can be calculated by following the simple division method:
Step 1: Divide 462 by 1, 462 ÷ 1 = 462.
Step 2: Continue dividing 462 by the numbers until the remainder becomes 0.
462 ÷ 1 = 462
462 ÷ 2 = 231
462 ÷ 3 = 154
462 ÷ 6 = 77
462 ÷ 7 = 66
462 ÷ 11 = 42
462 ÷ 14 = 33
462 ÷ 21 = 22
Therefore, the factors of 462 are: 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 462 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
462 ÷ 2 = 231
231 ÷ 3 = 77
77 ÷ 7 = 11
11 ÷ 11 = 1
The prime factors of 462 are 2, 3, 7, and 11.
The prime factorization of 462 is: 2 × 3 × 7 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 462 is divided by 2 to get 231.
Step 2: Now divide 231 by 3 to get 77.
Step 3: Then divide 77 by 7 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 462 is: 2 × 3 × 7 × 11.
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 462: (1, 462), (2, 231), (3, 154), (6, 77), (7, 66), (11, 42), (14, 33), (21, 22).
Negative factor pairs of 462: (-1, -462), (-2, -231), (-3, -154), (-6, -77), (-7, -66), (-11, -42), (-14, -33), (-21, -22).
Common Mistakes and How to Avoid Them in Factors of 462
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 462, 1 and 462 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 462 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 462/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 462 are prime numbers.
For example, 2, 3, 7, and 11 are the prime factors of 462, but it has other factors like 6, 21.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 462 as 2 × 3 × 7 × 11 and missing all the key factors.
Factors of 462 Examples
Problem 1
There are 77 students and 462 apples. How many apples will each student get if distributed equally?
They will get 6 apples each.
Explanation
To distribute the apples equally, we need to divide the total apples by the number of students.
462/77 = 6
Problem 2
A garden is rectangular, the length of the garden is 33 meters and the total area is 462 square meters. Find the width?
14 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
462 = 33 × width
To find the value of width, we need to shift 33 to the left side.
462/33 = width
Width = 14.
Problem 3
There are 11 buses and 462 passengers. How many passengers will be in each bus?
Each bus will have 42 passengers.
Explanation
To find the passengers in each bus, divide the total passengers by the buses.
462/11 = 42
Problem 4
In a school, there are 462 students, and 21 classes. How many students are there in each class?
There are 22 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
462/21 = 22
Problem 5
462 books need to be arranged in 66 shelves. How many books will go on each shelf?
Each of the shelves has 7 books.
Explanation
Divide total books by shelves.
462/66 = 7
FAQs on Factors of 462
1.What are the factors of 462?
2.Mention the prime factors of 462.
3.Is 462 a multiple of 7?
4.Mention the factor pairs of 462?
5.What is the square of 462?
6.How can children in Australia use numbers in everyday life to understand Factors of 462?
7.What are some fun ways kids in Australia can practice Factors of 462 with numbers?
8.What role do numbers and Factors of 462 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 462 skills?
Important Glossaries for Factors of 462
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, and 462.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 11 are prime factors of 462.
- 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 462 are (1, 462), (2, 231), etc.
- Prime factorization: Breaking down a number into a product of its prime factors. For 462, this is 2 × 3 × 7 × 11.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to give the original number. For 462, examples include (21, 22) and (7, 66).
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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
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