100 LearnersLast updated on May 26th, 2025
Factors of 1440
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 1440, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 1440?
The numbers that divide 1440 evenly are known as factors of 1440.
A factor of 1440 is a number that divides the number without remainder.
The factors of 1440 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 160, 180, 240, 288, 360, 480, 720, and 1440.
Negative factors of 1440: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -32, -36, -40, -45, -48, -60, -72, -80, -90, -120, -144, -160, -180, -240, -288, -360, -480, -720, and -1440.
Prime factors of 1440: 2, 3, and 5.
Prime factorization of 1440: 2^5 × 3^2 × 5.
The sum of factors of 1440: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 32 + 36 + 40 + 45 + 48 + 60 + 72 + 80 + 90 + 120 + 144 + 160 + 180 + 240 + 288 + 360 + 480 + 720 + 1440 = 4032
How to Find Factors of 1440?
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 1440. Identifying the numbers which are multiplied to get the number 1440 is the multiplication method.
Step 1: Multiply 1440 by 1, 1440 × 1 = 1440.
Step 2: Check for other numbers that give 1440 after multiplying
2 × 720 = 1440
3 × 480 = 1440
4 × 360 = 1440
5 × 288 = 1440
6 × 240 = 1440
8 × 180 = 1440
9 × 160 = 1440
10 × 144 = 1440
12 × 120 = 1440
15 × 96 = 1440
16 × 90 = 1440
18 × 80 = 1440
20 × 72 = 1440
24 × 60 = 1440
30 × 48 = 1440
32 × 45 = 1440
36 × 40 = 1440
Therefore, the positive factor pairs of 1440 are: (1, 1440), (2, 720), (3, 480), (4, 360), (5, 288), (6, 240), (8, 180), (9, 160), (10, 144), (12, 120), (15, 96), (16, 90), (18, 80), (20, 72), (24, 60), (30, 48), (32, 45), (36, 40).
All these factor pairs result in 1440.
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 1440 by 1, 1440 ÷ 1 = 1440.
Step 2: Continue dividing 1440 by the numbers until the remainder becomes 0.
1440 ÷ 1 = 1440
1440 ÷ 2 = 720
1440 ÷ 3 = 40
1440 ÷ 4 = 360
1440 ÷ 5 = 288
1440 ÷ 6 = 240
1440 ÷ 8 = 180
1440 ÷ 9 = 160
1440 ÷ 10 = 144
1440 ÷ 12 = 120
1440 ÷ 15 = 96
1440 ÷ 16 = 90
1440 ÷ 18 = 80
1440 ÷ 20 = 72
1440 ÷ 24 = 60
1440 ÷ 30 = 48
1440 ÷ 32 = 45
1440 ÷ 36 = 40
Therefore, the factors of 1440 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 160, 180, 240, 288, 360, 480, 720, and 1440.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 1440 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
1440 ÷ 2 = 720
720 ÷ 2 = 360
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 1440 are 2, 3, and 5.
The prime factorization of 1440 is: 2^5 × 3^2 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 1440 is divided by 2 to get 720.
Step 2: Now divide 720 by 2 to get 360.
Step 3: Then divide 360 by 2 to get 180.
Step 4: Divide 180 by 2 to get 90.
Step 5: Divide 90 by 2 to get 45.
Step 6: Divide 45 by 3 to get 15.
Step 7: Divide 15 by 3 to get 5.
Here, 5 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 1440 is: 2^5 × 3^2 × 5.
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 1440: (1, 1440), (2, 720), (3, 480), (4, 360), (5, 288), (6, 240), (8, 180), (9, 160), (10, 144), (12, 120), (15, 96), (16, 90), (18, 80), (20, 72), (24, 60), (30, 48), (32, 45), (36, 40).
Negative factor pairs of 1440: (-1, -1440), (-2, -720), (-3, -480), (-4, -360), (-5, -288), (-6, -240), (-8, -180), (-9, -160), (-10, -144), (-12, -120), (-15, -96), (-16, -90), (-18, -80), (-20, -72), (-24, -60), (-30, -48), (-32, -45), (-36, -40).
Common Mistakes and How to Avoid Them in Factors of 1440
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
People 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 1440, 1 and 1440 are also factors.
Factors of 1440 Examples
Problem 1
There are 12 workers and 1440 bricks. How will they divide the bricks equally?
They will get 120 bricks each.
Explanation
To divide the bricks equally, we need to divide the total bricks by the number of workers.
1440/12 = 120
Problem 2
A garden is rectangular, the length of the garden is 60 meters and the total area is 1440 square meters. Find the width?
24 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1440 = 60 × width
To find the value of width, divide
1440 by 60.
1440/60 = width
Width = 24.
Problem 3
There are 18 pallets and 1440 boxes. How many boxes will be on each pallet?
Each pallet will have 80 boxes.
Explanation
To find the number of boxes on each pallet, divide the total boxes by the number of pallets.
1440/18 = 80
Problem 4
In a competition, there are 1440 participants, and 45 groups. How many participants are there in each group?
There are 32 participants in each group.
Explanation
Dividing the participants by the total groups, we will get the number of participants in each group.
1440/45 = 32
Problem 5
1440 books need to be arranged in 36 boxes. How many books will go in each box?
Each of the boxes has 40 books.
Explanation
Divide total books by boxes.
1440/36 = 40
FAQs on Factors of 1440
1.What are the factors of 1440?
2.Mention the prime factors of 1440.
3.Is 1440 a multiple of 15?
4.Mention the factor pairs of 1440?
5.What is the square of 1440?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 1440?
7.What are some fun ways kids in United Kingdom can practice Factors of 1440 with numbers?
8.What role do numbers and Factors of 1440 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 1440 skills?
Important Glossaries for Factors of 1440
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1440 are 1, 2, 3, 4, 5, 6, 8, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 1440.
- 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 1440 are (1, 1440), (2, 720), etc.
- Prime factorization: Expressing a number as a product of its prime factors. For 1440, it is 2^5 × 3^2 × 5.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 1440 is a multiple of 15.
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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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