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Last updated on May 26th, 2025

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Factors of 690

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Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 690, how they are used in real life, and the tips to learn them quickly.

Factors of 690 for Thai Students
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What are the Factors of 690?

The numbers that divide 690 evenly are known as factors of 690.

 

A factor of 690 is a number that divides the number without remainder.

 

The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, and 690.

 

Negative factors of 690: -1, -2, -3, -5, -6, -10, -15, -23, -30, -46, -69, -115, -138, -230, -345, and -690.

 

Prime factors of 690: 2, 3, 5, and 23.

 

Prime factorization of 690: 2 × 3 × 5 × 23.

 

The sum of factors of 690: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 23 + 30 + 46 + 69 + 115 + 138 + 230 + 345 + 690 = 1728

factors of 690

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How to Find Factors of 690?

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 690. Identifying the numbers which are multiplied to get the number 690 is the multiplication method.

 

Step 1: Multiply 690 by 1, 690 × 1 = 690.

 

Step 2: Check for other numbers that give 690 after multiplying

 

2 × 345 = 690

3 × 230 = 690

5 × 138 = 690

6 × 115 = 690

10 × 69 = 690

15 × 46 = 690

23 × 30 = 690

 

Therefore, the positive factor pairs of 690 are: (1, 690), (2, 345), (3, 230), (5, 138), (6, 115), (10, 69), (15, 46), (23, 30).

 

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 690 by 1, 690 ÷ 1 = 690.

 

Step 2: Continue dividing 690 by the numbers until the remainder becomes 0.

 

690 ÷ 1 = 690

690 ÷ 2 = 345

690 ÷ 3 = 230

690 ÷ 5 = 138

690 ÷ 6 = 115

690 ÷ 10 = 69

690 ÷ 15 = 46

690 ÷ 23 = 30

 

Therefore, the factors of 690 are: 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690.

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Prime Factors and Prime Factorization

The factors can be found by dividing it with a prime number. 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 690 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

690 ÷ 2 = 345

345 ÷ 3 = 115

115 ÷ 5 = 23

23 ÷ 23 = 1

 

The prime factors of 690 are 2, 3, 5, and 23.

 

The prime factorization of 690 is: 2 × 3 × 5 × 23.

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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, 690 is divided by 2 to get 345.

 

Step 2: Now divide 345 by 3 to get 115.

 

Step 3: Then divide 115 by 5 to get 23. Here, 23 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 690 is: 2 × 3 × 5 × 23.

 

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 690: (1, 690), (2, 345), (3, 230), (5, 138), (6, 115), (10, 69), (15, 46), (23, 30).

 

Negative factor pairs of 690: (-1, -690), (-2, -345), (-3, -230), (-5, -138), (-6, -115), (-10, -69), (-15, -46), (-23, -30).

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Common Mistakes and How to Avoid Them in Factors of 690

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 word. Always remember to include 1 and the number itself.

 

For example, in factors of 690, 1 and 690 are also factors.

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Factors of 690 Examples

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Problem 1

There are 23 friends and 690 candies. How will they divide it equally?

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They will get 30 candies each.

Explanation

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

 

690/23 = 30

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Problem 2

A field is rectangular, the length of the field is 10 meters and the total area is 690 square meters. Find the width?

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69 meters.

Explanation

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

 

Area = length × width

 

690 = 10 × width

 

To find the value of width, we need to shift 10 to the left side.

 

690/10 = width

 

Width = 69.

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Problem 3

There are 46 bags and 690 apples. How many apples will be in each bag?

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Each bag will have 15 apples.

Explanation

To find the apples in each bag, divide the total apples with the bags.

 

690/46 = 15

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Problem 4

In a class, there are 690 students, and 30 groups. How many students are there in each group?

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There are 23 students in each group.

Explanation

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

 

690/30 = 23

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Problem 5

690 books need to be arranged in 230 shelves. How many books will go on each shelf?

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Each of the shelves has 3 books.

Explanation

Divide total books with shelves.

 

690/230 = 3

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FAQs on Factors of 690

1.What are the factors of 690?

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2.Mention the prime factors of 690.

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3.Is 690 a multiple of 6?

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4.Mention the factor pairs of 690.

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5.What is the square of 690?

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6.How can children in Thailand use numbers in everyday life to understand Factors of 690?

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7.What are some fun ways kids in Thailand can practice Factors of 690 with numbers?

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8.What role do numbers and Factors of 690 play in helping children in Thailand develop problem-solving skills?

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9.How can families in Thailand create number-rich environments to improve Factors of 690 skills?

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Important Glossaries for Factors of 690

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 690 are 1, 2, 3, 5, etc.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 23 are prime factors of 690.
     
  • 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 690 are (1, 690), (2, 345), etc.
     
  • Prime factorization: The expression of a number as a product of prime numbers. For example, the prime factorization of 690 is 2 × 3 × 5 × 23.
     
  • Multiplication method: A method used to find factor pairs by identifying numbers that multiply to a given number. For example, using multiplication to find that 2 × 345 = 690.
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About BrightChamps in Thailand

At BrightChamps, numbers are more than just figures—they open doors to endless possibilities! We support children all across Thailand in developing key math skills, focusing today on Factors of 690 with a special emphasis on factors—in an exciting, accessible, and fun way. Whether your child is figuring out the speed of a roller coaster at Dream World, keeping score at local football matches, or managing their allowance for the latest gadgets, knowing numbers builds their everyday confidence. Our interactive lessons make learning easy and enjoyable. Because kids in Thailand have unique learning styles, we tailor our approach to fit each child. From bustling Bangkok streets to the tropical islands of Phuket, BrightChamps makes math come alive all over Thailand. Let’s turn factors into a fun part of every child’s learning 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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Fun Fact

: She loves to read number jokes and games.

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