153 LearnersLast updated on May 29th, 2025
Factors of 1200
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 1200, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1200?
The numbers that divide 1200 evenly are known as factors of 1200.
A factor of 1200 is a number that divides the number without remainder.
The factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, and 1200.
Negative factors of 1200: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -100, -120, -150, -200, -240, -300, -400, -600, and -1200.
Prime factors of 1200: 2, 3, and 5.
Prime factorization of 1200: 24 × 3 × 52.
The sum of factors of 1200: 9336
How to Find Factors of 1200?
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 1200. Identifying the numbers which are multiplied to get the number 1200 is the multiplication method.
Step 1: Multiply 1200 by 1, 1200 × 1 = 1200.
Step 2: Check for other numbers that give 1200 after multiplying
2 × 600 = 1200
3 × 400 = 1200
4 × 300 = 1200
5 × 240 = 1200
6 × 200 = 1200
8 × 150 = 1200
10 × 120 = 1200
12 × 100 = 1200
15 × 80 = 1200
16 × 75 = 1200
20 × 60 = 1200
24 × 50 = 1200
25 × 48 = 1200
30 × 40 = 1200
Therefore, the positive factor pairs of 1200 are: (1, 1200), (2, 600), (3, 400), (4, 300), (5, 240), (6, 200), (8, 150), (10, 120), (12, 100), (15, 80), (16, 75), (20, 60), (24, 50), (25, 48), (30, 40).
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 simple division method -
Step 1: Divide 1200 by 1, 1200 ÷ 1 = 1200.
Step 2: Continue dividing 1200 by the numbers until the remainder becomes 0.
1200 ÷ 1 = 1200
1200 ÷ 2 = 600
1200 ÷ 3 = 400
1200 ÷ 4 = 300
1200 ÷ 5 = 240
1200 ÷ 6 = 200
1200 ÷ 8 = 150
1200 ÷ 10 = 120
1200 ÷ 12 = 100
1200 ÷ 15 = 80
1200 ÷ 16 = 75
1200 ÷ 20 = 60
1200 ÷ 24 = 50
1200 ÷ 25 = 48
1200 ÷ 30 = 40
Therefore, the factors of 1200 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200.
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 1200 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1200 ÷ 2 = 600
600 ÷ 2 = 300
300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 1200 are 2, 3, and 5.
The prime factorization of 1200 is: 24 × 3 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show -
Step 1: Firstly, 1200 is divided by 2 to get 600.
Step 2: Now divide 600 by 2 to get 300.
Step 3: Then divide 300 by 2 to get 150.
Step 4: Divide 150 by 2 to get 75.
Step 5: Divide 75 by 3 to get 25.
Step 6: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1200 is: 24 × 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 1200: (1, 1200), (2, 600), (3, 400), (4, 300), (5, 240), (6, 200), (8, 150), (10, 120), (12, 100), (15, 80), (16, 75), (20, 60), (24, 50), (25, 48), (30, 40).
Negative factor pairs of 1200: (-1, -1200), (-2, -600), (-3, -400), (-4, -300), (-5, -240), (-6, -200), (-8, -150), (-10, -120), (-12, -100), (-15, -80), (-16, -75), (-20, -60), (-24, -50), (-25, -48), (-30, -40).
Common Mistakes and How to Avoid Them in Factors of 1200
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 1200, 1 and 1200 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 1200 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 1200/1.5 = 800, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only primes.
For example, thinking all the factors of 1200 are prime numbers. For example, 2, 3, and 5 are the prime factors of 1200, 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 1200 as 24 × 3 × 52 and missing all the key factors.
Factors of 1200 Examples
Problem 1
There are 12 students and 1200 candies. How will they divide it equally?
They will get 100 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
1200/12 = 100
Problem 2
A garden is rectangular, the length of the garden is 30 meters and the total area is 1200 square meters. Find the width?
40 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width
1200 = 30 × width
To find the value of width, we need to shift 30 to the left side.
1200/30 = width
Width = 40.
Problem 3
There are 20 baskets and 1200 apples. How many apples will be in each basket?
Each basket will have 60 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
1200/20 = 60
Problem 4
In a class, there are 1200 students, and 25 groups. How many students are there in each group?
There are 48 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
1200/25 = 48
Problem 5
1200 books need to be arranged in 40 shelves. How many books will go on each shelf?
Each of the shelves has 30 books.
Explanation
Divide total books by shelves.
1200/40 = 30
FAQs on Factors of 1200
1.What are the factors of 1200?
2.Mention the prime factors of 1200.
3.Is 1200 a multiple of 15?
4.Mention the factor pairs of 1200?
5.What is the square of 1200?
6.How can children in United States use numbers in everyday life to understand Factors of 1200?
7.What are some fun ways kids in United States can practice Factors of 1200 with numbers?
8.What role do numbers and Factors of 1200 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1200 skills?
Important Glossaries for Factors of 1200
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1200 are 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 1200.
- 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 1200 are (1, 1200), (2, 600), etc.
- Multiples: A multiple is the product of a number and an integer. For example, 1200 is a multiple of 15.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1200 is 24 × 3 × 52.
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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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