135 LearnersLast updated on May 26th, 2025
Factors of 600
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 600, how they are used in real life, and tips to learn them quickly.
What are the Factors of 600?
The numbers that divide 600 evenly are known as factors of 600.
A factor of 600 is a number that divides the number without remainder.
The factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600.
Negative factors of 600: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -25, -30, -40, -50, -60, -75, -100, -120, -150, -200, -300, and -600.
Prime factors of 600: 2, 3, and 5.
Prime factorization of 600: 23 × 3 × 52.
The sum of factors of 600: 4032.
How to Find Factors of 600?
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 600. Identifying the numbers which are multiplied to get the number 600 is the multiplication method.
Step 1: Multiply 600 by 1, 600 × 1 = 600.
Step 2: Check for other numbers that give 600 after multiplying
2 × 300 = 600
3 × 200 = 600
4 × 150 = 600
5 × 120 = 600
6 × 100 = 600
8 × 75 = 600
10 × 60 = 600
12 × 50 = 600
15 × 40 = 600
20 × 30 = 600
Therefore, the positive factor pairs of 600 are: (1, 600), (2, 300), (3, 200), (4, 150), (5, 120), (6, 100), (8, 75), (10, 60), (12, 50), (15, 40), (20, 30). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers by 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 600 by 1, 600 ÷ 1 = 600.
Step 2: Continue dividing 600 by the numbers until the remainder becomes 0.
600 ÷ 1 = 600
600 ÷ 2 = 300
600 ÷ 3 = 200
600 ÷ 4 = 150
600 ÷ 5 = 120
600 ÷ 6 = 100
600 ÷ 8 = 75
600 ÷ 10 = 60
600 ÷ 12 = 50
600 ÷ 15 = 40
600 ÷ 20 = 30
Therefore, the factors of 600 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600.
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 600 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
600 ÷ 2 = 300
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 600 are 2, 3, and 5.
The prime factorization of 600 is: 2^3 × 3 × 5^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 600 is divided by 2 to get 300.
Step 2: Now divide 300 by 2 to get 150.
Step 3: Then divide 150 by 2 to get 75.
Step 4: Divide 75 by 3 to get 25.
Step 5: Divide 25 by 5 to get 5.
Here, 5 is the smallest prime number that cannot be divided further.
So, the prime factorization of 600 is: 23 × 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 600: (1, 600), (2, 300), (3, 200), (4, 150), (5, 120), (6, 100), (8, 75), (10, 60), (12, 50), (15, 40), (20, 30).
Negative factor pairs of 600: (-1, -600), (-2, -300), (-3, -200), (-4, -150), (-5, -120), (-6, -100), (-8, -75), (-10, -60), (-12, -50), (-15, -40), (-20, -30).
Common Mistakes and How to Avoid Them in Factors of 600
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 600, 1 and 600 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 600 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 600/1.5 = 400, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole number, not only just primes.
For example, thinking all the factors of 600 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 600, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 600 as 2^3 × 3 × 5^2 and missing all the key factors.
Factors of 600 Examples
Problem 1
There are 12 friends and 600 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 friends.
600/12 = 50
Problem 2
A field is rectangular, the length of the field is 25 meters and the total area is 600 square meters. Find the width?
24 meters.
Explanation
To find the width of the field, we use the formula,
Area = length × width
600 = 25 × width
To find the value of the width, we need to shift 25 to the left side.
600/25 = width
Width = 24.
Problem 3
There are 20 bags and 600 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.
600/20 = 30
Problem 4
In a class, there are 600 students, and 15 groups. How many students are there in each group?
There are 40 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
600/15 = 40
Problem 5
600 books need to be arranged in 24 shelves. How many books will go on each shelf?
Each of the shelves has 25 books.
Explanation
Divide total books by shelves.
600/24 = 25
FAQs on Factors of 600
1.What are the factors of 600?
2.Mention the prime factors of 600.
3.Is 600 a multiple of 4?
4.Mention the factor pairs of 600?
5.What is the square of 600?
6.How can children in Indonesia use numbers in everyday life to understand Factors of 600?
7.What are some fun ways kids in Indonesia can practice Factors of 600 with numbers?
8.What role do numbers and Factors of 600 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve Factors of 600 skills?
Important Glossaries for Factor of 600
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, and 600.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 600.
- 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 600 are (1, 600), (2, 300), etc.
- Multiple: A multiple is a product of a number and an integer. For example, 600 is a multiple of 4.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 600 is 2^3 × 3 × 5^2.
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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.
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