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Last updated on May 26th, 2025

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Factors of 462

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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.

Factors of 462 for UAE Students
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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 = 1160factors of 462

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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
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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.

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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.

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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.

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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).

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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

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Forgetting the number itself and 1 is a factor

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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.

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Factors of 462 Examples

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Problem 1

There are 77 students and 462 apples. How many apples will each student get if distributed equally?

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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

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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?

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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.

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Problem 3

There are 11 buses and 462 passengers. How many passengers will be in each bus?

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Each bus will have 42 passengers.

Explanation

To find the passengers in each bus, divide the total passengers by the buses.
462/11 = 42

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Problem 4

In a school, there are 462 students, and 21 classes. How many students are there in each class?

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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

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Problem 5

462 books need to be arranged in 66 shelves. How many books will go on each shelf?

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Each of the shelves has 7 books.

Explanation

Divide total books by shelves.
462/66 = 7

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FAQs on Factors of 462

1.What are the factors of 462?

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2.Mention the prime factors of 462.

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3.Is 462 a multiple of 7?

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4.Mention the factor pairs of 462?

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5.What is the square of 462?

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6.How can children in United Arab Emirates use numbers in everyday life to understand Factors of 462?

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7.What are some fun ways kids in United Arab Emirates can practice Factors of 462 with numbers?

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8.What role do numbers and Factors of 462 play in helping children in United Arab Emirates develop problem-solving skills?

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9.How can families in United Arab Emirates create number-rich environments to improve Factors of 462 skills?

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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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About BrightChamps in United Arab Emirates

At BrightChamps, numbers are more than just symbols—they open up a world of chances! We’re dedicated to helping children throughout the UAE build strong math skills, focusing today on Factors of 462 with an emphasis on factors—in a way that’s fun, clear, and engaging. Whether your child is figuring out the speed of a ride at Dubai Parks and Resorts, keeping track of local football scores, or managing their allowance for gadgets, mastering numbers builds everyday confidence. Our interactive lessons make learning straightforward and fun. Because kids in the UAE have different learning styles, we tailor our teaching to each child. From Dubai’s towering skyscrapers to Abu Dhabi’s cultural heritage, BrightChamps brings math to life across the UAE. Let’s turn factors into an exciting part of every child’s math journey!
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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.

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: She loves to read number jokes and games.

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