147 LearnersLast updated on May 26th, 2025
Factors of 969
Factors are the numbers that divide any given number evenly without a 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 969, how they are used in real life, and tips to learn them quickly.
What are the Factors of 969?
The numbers that divide 969 evenly are known as factors of 969.
A factor of 969 is a number that divides the number without remainder.
The factors of 969 are 1, 3, 17, 51, 19, 57, 323, and 969.
Negative factors of 969: -1, -3, -17, -51, -19, -57, -323, and -969.
Prime factors of 969: 3, 17, and 19.
Prime factorization of 969: 3 × 17 × 19.
The sum of factors of 969: 1 + 3 + 17 + 51 + 19 + 57 + 323 + 969 = 1440
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
How to Find Factors of 969?
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 969. Identifying the numbers which are multiplied to get the number 969 is the multiplication method.
Step 1: Multiply 969 by 1, 969 × 1 = 969.
Step 2: Check for other numbers that give 969 after multiplying
3 × 323 = 969
17 × 57 = 969
19 × 51 = 969
Therefore, the positive factor pairs of 969 are: (1, 969), (3, 323), (17, 57), (19, 51).
All these factor pairs result in 969.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 969 by 1, 969 ÷ 1 = 969.
Step 2: Continue dividing 969 by the numbers until the remainder becomes 0.
969 ÷ 1 = 969
969 ÷ 3 = 323
969 ÷ 17 = 57
969 ÷ 19 = 51
Therefore, the factors of 969 are: 1, 3, 17, 19, 51, 57, 323, 969.
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 969 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
969 ÷ 3 = 323
323 ÷ 17 = 19
19 ÷ 19 = 1
The prime factors of 969 are 3, 17, and 19.
The prime factorization of 969 is: 3 × 17 × 19.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 969 is divided by 3 to get 323.
Step 2: Now divide 323 by 17 to get 19.
Step 3: 19 is a prime number, so the process stops here. So, the prime factorization of 969 is: 3 × 17 × 19.
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 969: (1, 969), (3, 323), (17, 57), and (19, 51).
Negative factor pairs of 969: (-1, -969), (-3, -323), (-17, -57), and (-19, -51).
Common Mistakes and How to Avoid Them in Factors of 969
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 969, 1 and 969 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 969 consist of -1, -3, -17, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 969/1.5 = 646, 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 969 are prime numbers.
For example, 3, 17, and 19 are the prime factors of 969, but it has other factors like 51, 57.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 969 as 3 × 17 × 19 and missing all the key factors.
Level Up with a Math Certification!
2X Faster Learning (Grades 1-12)
Factors of 969 Examples
Problem 1
There are 969 apples to be distributed equally among 3 baskets. How many apples will each basket contain?
Each basket will contain 323 apples.
Explanation
To divide the apples equally, we need to divide the total apples by the number of baskets.
969/3 = 323
Problem 2
A rectangular field has an area of 969 square meters, with a length of 51 meters. What is the width?
19 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
969 = 51 × width
To find the value of width, we need to shift 51 to the left side.
969/51 = width
Width = 19.
Problem 3
There are 969 oranges and 57 people. How many oranges will each person get if distributed equally?
Each person will get 17 oranges.
Explanation
To find the oranges each person will get, divide the total oranges by the number of people.
969/57 = 17
Problem 4
In a class, there are 19 groups, and there are 969 students. How many students are there in each group?
There are 51 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
969/19 = 51
Problem 5
969 books need to be arranged in 323 shelves. How many books will go on each shelf?
Each shelf will have 3 books.
Explanation
Divide the total books by the number of shelves.
969/323 = 3
Turn your child into a math star!
#1 Math Hack Schools Won't Teach!
FAQs on Factors of 969
1.What are the factors of 969?
2.Mention the prime factors of 969.
3.Is 969 a multiple of 17?
4.Mention the factor pairs of 969?
5.What is the square of 969?
6.How can children in Qatar use numbers in everyday life to understand Factors of 969?
7.What are some fun ways kids in Qatar can practice Factors of 969 with numbers?
8.What role do numbers and Factors of 969 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 969 skills?
Struggling with Math?
Get 1:1 Coaching to Boost Grades Fast !
Important Glossaries for Factors of 969
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 969 are 1, 3, 17, 19, 51, 57, 323, and 969.
- Prime factors: The factors which are prime numbers. For example, 3, 17, and 19 are prime factors of 969.
- 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 969 are (1, 969), (3, 323), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 969 is 3 × 17 × 19.
- Multiple: A number that can be divided by another number without a remainder. For example, 969 is a multiple of 3, 17, and 19.
Explore More numbers
![Important Math Links Icon]()
Previous to Factors of 969
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.
