114 LearnersLast updated on May 26th, 2025
Factors of 690
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.
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
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
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.
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.
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.
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).
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
Forgetting the number itself and 1 is a factor
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.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 690 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 690/1.5 = 460, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 690 are prime numbers.
For example, 2, 3, 5, and 23 are the prime factors of 690, but it has other factors like 10, 46.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 690 as 2 × 3 × 5 × 23 and missing all the key factors.
Factors of 690 Examples
Problem 1
There are 23 friends and 690 candies. How will they divide it equally?
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
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?
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.
Problem 3
There are 46 bags and 690 apples. How many apples will be in each bag?
Each bag will have 15 apples.
Explanation
To find the apples in each bag, divide the total apples with the bags.
690/46 = 15
Problem 4
In a class, there are 690 students, and 30 groups. How many students are there in each group?
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
Problem 5
690 books need to be arranged in 230 shelves. How many books will go on each shelf?
Each of the shelves has 3 books.
Explanation
Divide total books with shelves.
690/230 = 3
FAQs on Factors of 690
1.What are the factors of 690?
2.Mention the prime factors of 690.
3.Is 690 a multiple of 6?
4.Mention the factor pairs of 690.
5.What is the square of 690?
6.How can children in Canada use numbers in everyday life to understand Factors of 690?
7.What are some fun ways kids in Canada can practice Factors of 690 with numbers?
8.What role do numbers and Factors of 690 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve Factors of 690 skills?
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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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.
