102 LearnersLast updated on May 26th, 2025
Factors of 975
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 975, how they are used in real life, and tips to learn them quickly.
What are the Factors of 975?
The numbers that divide 975 evenly are known as factors of 975.
A factor of 975 is a number that divides the number without a remainder.
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975.
Negative factors of 975: -1, -3, -5, -13, -15, -25, -39, -65, -75, -195, -325, and -975.
Prime factors of 975: 3, 5, and 13.
Prime factorization of 975: 3 × 52 × 13.
The sum of factors of 975: 1 + 3 + 5 + 13 + 15 + 25 + 39 + 65 + 75 + 195 + 325 + 975 = 1736
How to Find Factors of 975?
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 975. Identifying the numbers that are multiplied to get the number 975 is the multiplication method.
Step 1: Multiply 975 by 1, 975 × 1 = 975.
Step 2: Check for other numbers that give 975 after multiplying
3 × 325 = 975
5 × 195 = 975
13 × 75 = 975
15 × 65 = 975
25 × 39 = 975
Therefore, the positive factor pairs of 975 are: (1, 975), (3, 325), (5, 195), (13, 75), (15, 65), (25, 39).
All these factor pairs result in 975.
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 975 by 1, 975 ÷ 1 = 975.
Step 2: Continue dividing 975 by the numbers until the remainder becomes 0.
975 ÷ 1 = 975
975 ÷ 3 = 325
975 ÷ 5 = 195
975 ÷ 13 = 75
975 ÷ 15 = 65
975 ÷ 25 = 39
Therefore, the factors of 975 are: 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 975 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
975 ÷ 3 = 325
325 ÷ 5 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
The prime factors of 975 are 3, 5, and 13.
The prime factorization of 975 is: 3 × 5^2 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 975 is divided by 3 to get 325.
Step 2: Now divide 325 by 5 to get 65.
Step 3: Then divide 65 by 5 to get 13.
Here, 13 is the smallest prime number, and it cannot be divided anymore.
So, the prime factorization of 975 is: 3 × 52 × 13.
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 975: (1, 975), (3, 325), (5, 195), (13, 75), (15, 65), and (25, 39).
Negative factor pairs of 975: (-1, -975), (-3, -325), (-5, -195), (-13, -75), (-15, -65), and (-25, -39).
Common Mistakes and How to Avoid Them in Factors of 975
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 975, 1 and 975 are also factors.
Factors of 975 Examples
Problem 1
There are 13 teams and 975 players. How will they divide it equally?
They will get 75 players each.
Explanation
To divide the players equally, we need to divide the total players by the number of teams.
975/13 = 75
Problem 2
A garden is rectangular, the length of the garden is 15 meters and the total area is 975 square meters. Find the width?
65 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
975 = 15 × width
To find the value of width, we need to shift 15 to the left side.
975/15 = width
Width = 65.
Problem 3
There are 5 baskets and 975 apples. How many apples will be in each basket?
Each basket will have 195 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
975/5 = 195
Problem 4
In a hall, there are 975 chairs, and 25 rows. How many chairs are there in each row?
There are 39 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
975/25 = 39
Problem 5
975 tickets need to be distributed in 3 booths. How many tickets will go to each booth?
Each of the booths has 325 tickets.
Explanation
Divide total tickets by booths.
975/3 = 325
FAQs on Factors of 975
1.What are the factors of 975?
2.Mention the prime factors of 975.
3.Is 975, a multiple of 5?
4.Mention the factor pairs of 975?
5.What is the square of 975?
6.How can children in Qatar use numbers in everyday life to understand Factors of 975?
7.What are some fun ways kids in Qatar can practice Factors of 975 with numbers?
8.What role do numbers and Factors of 975 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 975 skills?
Important Glossaries for Factor of 975
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, and 975.
- Prime factors: The factors which are prime numbers. For example, 3, 5, and 13 are prime factors of 975.
- 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 975 are (1, 975), (3, 325), etc.
- Prime factorization: The process of determining the prime factors of a number. For example, the prime factorization of 975 is 3 × 52 × 13.
- Multiples: A number that can be divided by another number without a remainder. For example, 975 is a multiple of 5.
Explore More numbers
Previous to Factors of 975
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.
