Last updated on May 29th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 12 students and 1200 candies. How will they divide it equally?
They will get 100 candies each.
To divide the candies equally, we need to divide the total candies by the number of students.
1200/12 = 100
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.
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.
There are 20 baskets and 1200 apples. How many apples will be in each basket?
Each basket will have 60 apples.
To find the apples in each basket, divide the total apples by the baskets.
1200/20 = 60
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.
Dividing the students by the total groups, we will get the number of students in each group.
1200/25 = 48
1200 books need to be arranged in 40 shelves. How many books will go on each shelf?
Each of the shelves has 30 books.
Divide total books by shelves.
1200/40 = 30
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.
: She loves to read number jokes and games.