Factors of 464
2026-02-21 20:44 Diff
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Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without 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 464, how they are used in real life, and tips to learn them quickly.

What are the Factors of 464?

The numbers that divide 464 evenly are known as factors of 464. A factor of 464 is a number that divides the number without remainder.

The factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, and 464.

Negative factors of 464: -1, -2, -4, -8, -16, -29, -58, -116, -232, and -464.

Prime factors of 464: 2 and 29.

Prime factorization of 464: 2^4 × 29.

The sum of factors of 464: 1 + 2 + 4 + 8 + 16 + 29 + 58 + 116 + 232 + 464 = 930

How to Find Factors of 464?

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 464. Identifying the numbers which are multiplied to get the number 464 is the multiplication method.

Step 1: Multiply 464 by 1, 464 × 1 = 464.

Step 2: Check for other numbers that give 464 after multiplying

2 × 232 = 464

4 × 116 = 464

8 × 58 = 464

16 × 29 = 464

Therefore, the positive factor pairs of 464 are: (1, 464), (2, 232), (4, 116), (8, 58), (16, 29). All these factor pairs result in 464.

For every positive factor, there is a negative factor.

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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 464 by 1, 464 ÷ 1 = 464.

Step 2: Continue dividing 464 by the numbers until the remainder becomes 0.

464 ÷ 1 = 464

464 ÷ 2 = 232

464 ÷ 4 = 116

464 ÷ 8 = 58

464 ÷ 16 = 29

Therefore, the factors of 464 are: 1, 2, 4, 8, 16, 29, 58, 116, 232, 464.

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: In this process, prime factors of 464 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

464 ÷ 2 = 232

232 ÷ 2 = 116

116 ÷ 2 = 58

58 ÷ 2 = 29

29 ÷ 29 = 1

The prime factors of 464 are 2 and 29. The prime factorization of 464 is: 24 × 29.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 464 is divided by 2 to get 232.

Step 2: Now divide 232 by 2 to get 116.

Step 3: Then divide 116 by 2 to get 58.

Step 4: Divide 58 by 2 to get 29.

Here, 29 is the smallest prime number, that cannot be divided anymore.

So, the prime factorization of 464 is: 24 × 29.

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 464: (1, 464), (2, 232), (4, 116), (8, 58), and (16, 29).

Negative factor pairs of 464: (-1, -464), (-2, -232), (-4, -116), (-8, -58), and (-16, -29).

Common Mistakes and How to Avoid Them in Factors of 464

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 16 boxes and 464 pencils. How will they divide them equally?

Okay, lets begin

They will get 29 pencils each.

Explanation

To divide the pencils equally, we need to divide the total pencils with the number of boxes. 464/16 = 29

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Problem 2

A garden is rectangular, the length of the garden is 29 meters and the total area is 464 square meters. Find the width?

Okay, lets begin

16 meters.

Explanation

To find the width of the garden, we use the formula, Area = length × width 464 = 29 × width To find the value of width, we need to shift 29 to the left side. 464/29 = width Width = 16.

Well explained 👍

Problem 3

There are 8 teams and 464 players. How many players will be in each team?

Okay, lets begin

Each team will have 58 players.

Explanation

To find the players in each team, divide the total players with the teams. 464/8 = 58

Well explained 👍

Problem 4

In a school, there are 464 students, and 58 classes. How many students are there in each class?

Okay, lets begin

There are 8 students in each class.

Explanation

Dividing the students with the total classes, we will get the number of students in each class. 464/58 = 8

Well explained 👍

Problem 5

464 chairs need to be arranged in 4 rows. How many chairs will go in each row?

Okay, lets begin

Each of the rows has 116 chairs.

Explanation

Divide total chairs with rows. 464/4 = 116

Well explained 👍

FAQs on Factors of 464

1.What are the factors of 464?

1, 2, 4, 8, 16, 29, 58, 116, 232, 464 are the factors of 464.

2.Mention the prime factors of 464.

The prime factors of 464 are 2^4 × 29.

3.Is 464 a multiple of 4?

4.Mention the factor pairs of 464?

(1, 464), (2, 232), (4, 116), (8, 58), and (16, 29) are the factor pairs of 464.

5.What is the square of 464?

Important Glossaries for Factor of 464

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 464 are 1, 2, 4, 8, 16, 29, 58, 116, 232, and 464.
  • Prime factors: The factors which are prime numbers. For example, 2 and 29 are prime factors of 464.
  • 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 464 are (1, 464), (2, 232), etc.
  • Prime factorization: Decomposition of a number into a product of prime numbers. For example, the prime factorization of 464 is 24 × 29.
  • Multiple: A multiple is the result of multiplying a number by an integer. For example, 464 is a multiple of 2.

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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.