Factors of 689
2026-02-28 17:46 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-689

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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 689, how they are used in real life, and tips to learn them quickly.

What are the Factors of 689?

The numbers that divide 689 evenly are known as factors of 689.

A factor of 689 is a number that divides the number without remainder.

The factors of 689 are 1, 13, 53, and 689.

Negative factors of 689: -1, -13, -53, and -689.

Prime factors of 689: 13 and 53.

Prime factorization of 689: 13 × 53.

The sum of factors of 689: 1 + 13 + 53 + 689 = 756

How to Find Factors of 689?

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 689. Identifying the numbers which are multiplied to get the number 689 is the multiplication method.

Step 1: Multiply 689 by 1, 689 × 1 = 689.

Step 2: Check for other numbers that give 689 after multiplying 13 × 53 = 689

Therefore, the positive factor pairs of 689 are: (1, 689), (13, 53).

All these factor pairs result in 689.

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 a simple division method

Step 1: Divide 689 by 1, 689 ÷ 1 = 689.

Step 2: Continue dividing 689 by the numbers until the remainder becomes 0.

689 ÷ 1 = 689

689 ÷ 13 = 53

689 ÷ 53 = 13

Therefore, the factors of 689 are: 1, 13, 53, 689.

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 689 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

689 ÷ 13 = 53

53 ÷ 53 = 1

The prime factors of 689 are 13 and 53.

The prime factorization of 689 is: 13 × 53.

Factor Tree

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

Step 1: Firstly, 689 is divided by 13 to get 53.

Step 2: Now divide 53 by 53 to get 1. Here, 53 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 689 is: 13 × 53.

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 689: (1, 689), (13, 53).

Negative factor pairs of 689: (-1, -689), (-13, -53).

Common Mistakes and How to Avoid Them in Factors of 689

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 13 friends and 689 apples. How will they divide it equally?

Okay, lets begin

They will get 53 apples each.

Explanation

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

689/13 = 53

Well explained 👍

Problem 2

A field is rectangular, the length of the field is 53 meters and the total area is 689 square meters. Find the width?

Okay, lets begin

13 meters.

Explanation

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

Area = length × width

689 = 53 × width

To find the value of width, we need to shift 53 to the left side.

689/53 = width

Width = 13.

Well explained 👍

Problem 3

There are 53 boxes and 689 marbles. How many marbles will be in each box?

Okay, lets begin

Each box will have 13 marbles.

Explanation

To find the marbles in each box, divide the total marbles by the boxes.

689/53 = 13

Well explained 👍

Problem 4

In a class, there are 689 students, and 1 group. How many students are there in the group?

Okay, lets begin

There are 689 students in the group.

Explanation

Dividing the students by the total groups, we will get the number of students in each group.

689/1 = 689

Well explained 👍

Problem 5

689 pages need to be arranged in 53 folders. How many pages will go in each folder?

Okay, lets begin

Each of the folders has 13 pages.

Explanation

Divide total pages by folders.

689/53 = 13

Well explained 👍

FAQs on Factors of 689

1.What are the factors of 689?

1, 13, 53, 689 are the factors of 689.

2.Mention the prime factors of 689.

The prime factors of 689 are 13 × 53.

3.Is 689 a multiple of 13?

4.Mention the factor pairs of 689?

(1, 689), (13, 53) are the factor pairs of 689.

5.What is the square of 689?

Important Glossaries for Factor of 689

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 689 are 1, 13, 53, and 689.
     
  • Prime factors: The factors which are prime numbers. For example, 13 and 53 are prime factors of 689.
     
  • 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 689 are (1, 689), (13, 53).
     
  • Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 689 is 13 × 53.
     
  • Multiple: A number that can be divided by another number without leaving a remainder. For example, 689 is a multiple of 13.

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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.