118 LearnersLast updated on May 26th, 2025
Factors of 689
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.
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
- Using factor tree
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.
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 number. Always remember to include 1 and the number itself.
For example, in factors of 689, 1 and 689 is also a factor.
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 689 consist of -1, -13, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 689/1.5 = 459.333, 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 689 are prime numbers.
For example, 13 and 53 are the prime factors of 689, but it has other factors like 1, 689.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, Not breaking 689 as 13 × 53 and missing all the key factors.
Factors of 689 Examples
Problem 1
There are 13 friends and 689 apples. How will they divide it equally?
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
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?
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.
Problem 3
There are 53 boxes and 689 marbles. How many marbles will be in each box?
Each box will have 13 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
689/53 = 13
Problem 4
In a class, there are 689 students, and 1 group. How many students are there in the group?
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
Problem 5
689 pages need to be arranged in 53 folders. How many pages will go in each folder?
Each of the folders has 13 pages.
Explanation
Divide total pages by folders.
689/53 = 13
FAQs on Factors of 689
1.What are the factors of 689?
2.Mention the prime factors of 689.
3.Is 689 a multiple of 13?
4.Mention the factor pairs of 689?
5.What is the square of 689?
6.How can children in Qatar use numbers in everyday life to understand Factors of 689?
7.What are some fun ways kids in Qatar can practice Factors of 689 with numbers?
8.What role do numbers and Factors of 689 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 689 skills?
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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About BrightChamps in Qatar
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.
