102 LearnersLast updated on May 26th, 2025
Factors of 750
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 750, how they are used in real life, and tips to learn them quickly.
What are the Factors of 750?
The numbers that divide 750 evenly are known as factors of 750.
A factor of 750 is a number that divides the number without a remainder.
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750.
Negative factors of 750: -1, -2, -3, -5, -6, -10, -15, -25, -30, -50, -75, -125, -150, -250, -375, and -750.
Prime factors of 750: 2, 3, and 5.
Prime factorization of 750: 2 × 3 × 5³.
The sum of factors of 750: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 25 + 30 + 50 + 75 + 125 + 150 + 250 + 375 + 750 = 1872
How to Find Factors of 750?
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 750. Identifying the numbers which are multiplied to get the number 750 is the multiplication method.
Step 1: Multiply 750 by 1, 750 × 1 = 750.
Step 2: Check for other numbers that give 750 after multiplying
3 × 250 = 750
5 × 150 = 750
10 × 75 = 750
15 × 50 = 750
25 × 30 = 750
Therefore, the positive factor pairs of 750 are: (1, 750), (3, 250), (5, 150), (10, 75), (15, 50), (25, 30). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number with whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 750 by 1, 750 ÷ 1 = 750.
Step 2: Continue dividing 750 by the numbers until the remainder becomes 0.
750 ÷ 1 = 750
750 ÷ 2 = 375
750 ÷ 3 = 250
750 ÷ 5 = 150
750 ÷ 6 = 125
750 ÷ 10 = 75
750 ÷ 15 = 50
750 ÷ 25 = 30
Therefore, the factors of 750 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750.
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 750 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
750 ÷ 2 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 750 are 2, 3, and 5. The prime factorization of 750 is: 2 × 3 × 5³.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 750 is divided by 2 to get 375.
Step 2: Now divide 375 by 3 to get 125.
Step 3: Then divide 125 by 5 to get 25.
Step 4: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 750 is: 2 × 3 × 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 750: (1, 750), (3, 250), (5, 150), (10, 75), (15, 50), (25, 30).
Negative factor pairs of 750: (-1, -750), (-3, -250), (-5, -150), (-10, -75), (-15, -50), (-25, -30).
Common Mistakes and How to Avoid Them in Factors of 750
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 750, 1 and 750 are also factors.
Factors of 750 Examples
Problem 1
There are 15 students and 750 candies. How will they divide it equally?
They will get 50 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
750/15 = 50
Problem 2
A rectangular garden has a length of 25 meters and a total area of 750 square meters. Find the width.
30 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
750 = 25 × width
To find the value of width, we need to divide 750 by 25.
750/25 = width
Width = 30.
Problem 3
There are 25 baskets and 750 apples. How many apples will be in each basket?
Each basket will have 30 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
750/25 = 30
Problem 4
In a school, there are 750 students, and 50 groups. How many students are there in each group?
There are 15 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
750/50 = 15
Problem 5
750 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each of the shelves has 50 books.
Explanation
Divide total books by shelves.
750/15 = 50
FAQs on Factors of 750
1.What are the factors of 750?
2.Mention the prime factors of 750.
3.Is 750 a multiple of 5?
4.Mention the factor pairs of 750.
5.What is the square of 750?
6.How can children in India use numbers in everyday life to understand Factors of 750?
7.What are some fun ways kids in India can practice Factors of 750 with numbers?
8.What role do numbers and Factors of 750 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 750 skills?
Important Glossaries for Factors of 750
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, and 750.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 750.
- 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 750 are (1, 750), (3, 250), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 750 is 2 × 3 × 5³.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, 5 × 150 = 750.
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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.
