Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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 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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 969 apples to be distributed equally among 3 baskets. How many apples will each basket contain?
Each basket will contain 323 apples.
To divide the apples equally, we need to divide the total apples by the number of baskets.
969/3 = 323
A rectangular field has an area of 969 square meters, with a length of 51 meters. What is the width?
19 meters.
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.
There are 969 oranges and 57 people. How many oranges will each person get if distributed equally?
Each person will get 17 oranges.
To find the oranges each person will get, divide the total oranges by the number of people.
969/57 = 17
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.
Dividing the students by the total groups, we will get the number of students in each group.
969/19 = 51
969 books need to be arranged in 323 shelves. How many books will go on each shelf?
Each shelf will have 3 books.
Divide the total books by the number of shelves.
969/323 = 3
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.
: She loves to read number jokes and games.