Factors of 8400
2026-02-28 23:42 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 8400, how they are used in real life, and the tips to learn them quickly.

What are the Factors of 8400?

The numbers that divide 8400 evenly are known as factors of 8400.

A factor of 8400 is a number that divides the number without remainder.

The factors of 8400 include several numbers like 1, 2, 3, 4, 5, 6, 7, 8, and so on up to 8400.

Negative factors of 8400 include: -1, -2, -3, -4, -5, -6, -7, -8, and so on.

Prime factors of 8400: 2, 3, 5, and 7.

Prime factorization of 8400: 24 × 3 × 52 × 7.

The sum of factors of 8400: Calculating the sum requires summing all positive factors.

How to Find Factors of 8400?

Factors can be found using different methods. Mentioned below are some commonly used methods: 

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 8400. Identifying the numbers which are multiplied to get the number 8400 is the multiplication method.

Step 1: Multiply 8400 by 1, 8400 × 1 = 8400.

Step 2: Check for other numbers that give 8400 after multiplying.

For example, 2 × 4200 = 84003 × 2800 = 8400, etc.

Therefore, the positive factor pairs of 8400 are (1, 8400), (2, 4200), (3, 2800), and so on.

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 as whole numbers as factors. Factors can be calculated by following a simple division method 

Step 1: Divide 8400 by 1, 8400 ÷ 1 = 8400.

Step 2: Continue dividing 8400 by the numbers until the remainder becomes 0.

For example, 8400 ÷ 2 = 4200, 8400 ÷ 3 = 2800, etc.

Therefore, the factors of 8400 include numbers like 1, 2, 3, 4, 5, 6, 7, 8, and so on.

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: In this process, prime factors of 8400 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

8400 ÷ 2 = 4200

4200 ÷ 2 = 2100

2100 ÷ 2 = 1050

1050 ÷ 2 = 525

525 ÷ 3 = 175

175 ÷ 5 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

The prime factors of 8400 are 2, 3, 5, and 7.

The prime factorization of 8400 is: 24 × 3 × 52 × 7.

Factor Tree

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

Step 1: Firstly, 8400 is divided by 2 to get 4200.

Step 2: Now divide 4200 by 2 to get 2100.

Step 3: Then divide 2100 by 2 to get 1050.

Step 4: Divide 1050 by 2 to get 525.

Step 5: Divide 525 by 3 to get 175.

Step 6: Divide 175 by 5 to get 35.

Step 7: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore.

So, the prime factorization of 8400 is: 24 × 3 × 52 × 7.

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 8400 include: (1, 8400), (2, 4200), (3, 2800), etc.

Negative factor pairs of 8400 include: (-1, -8400), (-2, -4200), (-3, -2800), etc.

Common Mistakes and How to Avoid Them in Factors of 8400

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 420 friends and 8400 candies. How will they divide them equally?

Okay, lets begin

They will get 20 candies each.

Explanation

To divide the candies equally, we need to divide the total candies with the number of friends. 8400/420 = 20

Well explained 👍

Problem 2

A field is rectangular, the length of the field is 120 meters, and the total area is 8400 square meters. Find the width?

Okay, lets begin

70 meters.

Explanation

To find the width of the field, we use the formula,

Area = length × width

8400 = 120 × width

To find the value of width, we need to shift 120 to the left side.

8400/120 = width

Width = 70.

Well explained 👍

Problem 3

There are 80 bags and 8400 marbles. How many marbles will be in each bag?

Okay, lets begin

Each bag will have 105 marbles.

Explanation

To find the marbles in each bag, divide the total marbles with the bags. 8400/80 = 105

Well explained 👍

Problem 4

In a class, there are 8400 students, and 210 groups. How many students are there in each group?

Okay, lets begin

There are 40 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group. 8400/210 = 40

Well explained 👍

Problem 5

8400 books need to be arranged in 150 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 56 books.

Explanation

Divide total books with shelves. 8400/150 = 56

Well explained 👍

FAQs on Factors of 8400

1.What are the factors of 8400?

The factors of 8400 include numbers like 1, 2, 3, 4, 5, 6, 7, 8, and so on up to 8400.

2.Mention the prime factors of 8400.

The prime factors of 8400 are 24 × 3 × 52 × 7.

3.Is 8400 a multiple of 4?

4.Mention the factor pairs of 8400?

Factor pairs of 8400 include: (1, 8400), (2, 4200), (3, 2800), etc.

5.What is the square of 8400?

The square of 8400 is 70,560,000.

Important Glossaries for Factors of 8400

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 8400 include numbers like 1, 2, 3, 4, etc.
  • Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 7 are prime factors of 8400.
  • 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 8400 are (1, 8400), (2, 4200), etc.
  • Prime factorization: Writing a number as the product of its prime factors. For example, the prime factorization of 8400 is 24 × 3 × 52 × 7.
  • Multiples: The result of multiplying a number by an integer. For example, 8400 is a multiple of 2, 3, 4, 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.