Factors of 867
2026-02-21 20:27 Diff
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Last updated on December 12, 2025

Factors are numbers that divide a given number evenly without any remainder. In everyday life, we use factors for tasks such as dividing items equally and organizing objects efficiently. In this topic, we will explore the factors of 867, their practical applications, and some tips for learning them quickly.

What are the Factors of 867?

The numbers that divide 867 evenly are known as factors of 867.

A factor of 867 is a number that divides the number without leaving a remainder.

The factors of 867 are 1, 3, 17, 51, 289, and 867.

Negative factors of 867: -1, -3, -17, -51, -289, and -867.

Prime factors of 867: 3 and 17.

Prime factorization of 867: 3 × 17 × 17.

The sum of factors of 867: 1 + 3 + 17 + 51 + 289 + 867 = 1228

How to Find Factors of 867?

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify pairs of numbers that multiply to give 867. Identifying the numbers that are multiplied to get 867 is the multiplication method.

Step 1: Multiply 867 by 1, 867 × 1 = 867.

Step 2: Check for other numbers that give 867 when multiplied:

3 × 289 = 867

17 × 51 = 867

Therefore, the positive factor pairs of 867 are: (1, 867), (3, 289), (17, 51).

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given number by whole numbers until the remainder becomes zero and listing out the numbers that result in whole numbers as factors. Factors can be calculated by following a simple division method

Step 1: Divide 867 by 1, 867 ÷ 1 = 867.

Step 2: Continue dividing 867 by numbers until the remainder becomes 0.

867 ÷ 1 = 867

867 ÷ 3 = 289

867 ÷ 17 = 51

Therefore, the factors of 867 are: 1, 3, 17, 51, 289, 867.

Prime Factors and Prime Factorization

Factors can be found by dividing the number with prime numbers. We can find the prime factors using the following methods:

Using Prime Factorization: In this process, prime factors of 867 divide the number to break it down into the multiplication form of prime factors until the remainder becomes 1.

867 ÷ 3 = 289

289 ÷ 17 = 17

17 ÷ 17 = 1

The prime factors of 867 are 3 and 17.

The prime factorization of 867 is: 3 × 17 × 17.

Factor Tree

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

Step 1: Firstly, 867 is divided by 3 to get 289.

Step 2: Now divide 289 by 17 to get 17.

Step 3: Here, 17 is a prime number that cannot be divided further. So, the prime factorization of 867 is: 3 × 17 × 17.

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 867: (1, 867), (3, 289), (17, 51).

Negative factor pairs of 867: (-1, -867), (-3, -289), (-17, -51).

Common Mistakes and How to Avoid Them in Factors of 867

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 9 friends and 867 candies. How will they divide them equally?

Okay, lets begin

They will get 96 candies each, with 3 candies left over.

Explanation

To divide the candies equally, we need to divide the total candies by the number of friends.

867 ÷ 9 = 96 R3

Well explained 👍

Problem 2

A garden is rectangular, the length of the garden is 51 meters and the total area is 867 square meters. Find the width.

Okay, lets begin

17 meters.

Explanation

To find the width of the garden, we use the formula, Area = length × width

867 = 51 × width

To find the value of the width, we need to divide 867 by 51.

867 ÷ 51 = width

Width = 17.

Well explained 👍

Problem 3

There are 17 baskets and 867 apples. How many apples will be in each basket?

Okay, lets begin

Each basket will have 51 apples.

Explanation

To find the apples in each basket, divide the total apples by the number of baskets.

867 ÷ 17 = 51

Well explained 👍

Problem 4

In a school, there are 867 students and 51 classes. How many students are there in each class?

Okay, lets begin

There are 17 students in each class.

Explanation

Dividing the students by the total classes, we will get the number of students in each class.

867 ÷ 51 = 17

Well explained 👍

Problem 5

867 pages need to be distributed in 3 binders. How many pages will go in each binder?

Okay, lets begin

Each binder will have 289 pages.

Explanation

Divide the total pages by the number of binders.

867 ÷ 3 = 289

Well explained 👍

FAQs on Factors of 867

1.What are the factors of 867?

1, 3, 17, 51, 289, 867 are the factors of 867.

2.Mention the prime factors of 867.

The prime factors of 867 are 3 × 17 × 17.

3.Is 867 a multiple of 3?

4.Mention the factor pairs of 867.

(1, 867), (3, 289), (17, 51) are the factor pairs of 867.

5.What is the square of 867?

Important Glossaries for Factors of 867

  • Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 867 are 1, 3, 17, 51, 289, and 867.
  • Prime Factors: Factors that are prime numbers. For example, 3 and 17 are prime factors of 867.
  • Factor Pairs: Two numbers in a pair that are multiplied to give the original number. For example, the factor pairs of 867 are (1, 867), (3, 289), (17, 51).
  • Multiplication Method: A method to find factors by identifying pairs that multiply to give the number.
  • Division Method: A method to find factors by dividing the number by integers until the remainder is zero.

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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.