100 LearnersLast updated on May 26th, 2025
Factors of 300
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 300, how they are used in real life, and tips to learn them quickly.
What are the Factors of 300?
The numbers that divide 300 evenly are known as factors of 300.
A factor of 300 is a number that divides the number without remainder.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
Negative factors of 300: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -150, and -300.
Prime factors of 300: 2, 3, and 5.
Prime factorization of 300: 2² × 3 × 5².
The sum of factors of 300: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 25 + 30 + 50 + 60 + 75 + 100 + 150 + 300 = 868
How to Find Factors of 300?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 300. Identifying the numbers which are multiplied to get the number 300 is the multiplication method.
Step 1: Multiply 300 by 1, 300 × 1 = 300.
Step 2: Check for other numbers that give 300 after multiplying
2 × 150 = 300
3 × 100 = 300
4 × 75 = 300
5 × 60 = 300
6 × 50 = 300
10 × 30 = 300
12 × 25 = 300
15 × 20 = 300
Therefore, the positive factor pairs of 300 are: (1, 300), (2, 150), (3, 100), (4, 75), (5, 60), (6, 50), (10, 30), (12, 25), and (15, 20).
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 300 by 1, 300 ÷ 1 = 300.
Step 2: Continue dividing 300 by the numbers until the remainder becomes 0.
300 ÷ 1 = 300
300 ÷ 2 = 150
300 ÷ 3 = 100
300 ÷ 4 = 75
300 ÷ 5 = 60
300 ÷ 6 = 50
300 ÷ 10 = 30
300 ÷ 12 = 25
300 ÷ 15 = 20
Therefore, the factors of 300 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
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 300 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 300 are 2, 3, and 5.
The prime factorization of 300 is: 2² × 3 × 5².
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 300 is divided by 2 to get 150.
Step 2: Now divide 150 by 2 to get 75.
Step 3: Then divide 75 by 3 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 300 is: 2² × 3 × 5².
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 300: (1, 300), (2, 150), (3, 100), (4, 75), (5, 60), (6, 50), (10, 30), (12, 25), (15, 20).
Negative factor pairs of 300: (-1, -300), (-2, -150), (-3, -100), (-4, -75), (-5, -60), (-6, -50), (-10, -30), (-12, -25), (-15, -20).
Common Mistakes and How to Avoid Them in Factors of 300
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 300, 1 and 300 are also factors.
Factors of 300 Examples
Problem 1
There are 15 friends and 300 candies. How will they divide it equally?
They will get 20 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
300/15 = 20
Problem 2
A piece of land is rectangular, the length of the field is 25 meters and the total area is 300 square meters. Find the width?
12 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
300 = 25 × width
To find the value of width, we need to shift 25 to the left side.
300/25 = width
Width = 12.
Problem 3
There are 10 bags and 300 marbles. How many marbles will be in each bag?
Each bag will have 30 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the bags.
300/10 = 30
Problem 4
In a class, there are 300 students, and 12 groups. How many students are there in each group?
There are 25 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
300/12 = 25
Problem 5
300 books need to be arranged in 5 shelves. How many books will go on each shelf?
Each of the shelves has 60 books.
Explanation
Divide total books by shelves.
300/5 = 60
FAQs on Factors of 300
1.What are the factors of 300?
2.Mention the prime factors of 300.
3.Is 300 a multiple of 10?
4.Mention the factor pairs of 300?
5.What is the square of 300?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 300?
7.What are some fun ways kids in Bahrain can practice Factors of 300 with numbers?
8.What role do numbers and Factors of 300 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 300 skills?
Important Glossaries for Factor of 300
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, and 300.
- Prime Factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 300.
- 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 300 are (1, 300), (2, 150), etc.
- Prime Factorization: Expressing a number as the product of its prime numbers. For example, the prime factorization of 300 is 2² × 3 × 5².
- Multiple: A number that can be divided by another number without a remainder. For example, 300 is a multiple of 10.
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About BrightChamps in Bahrain
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.
