421 LearnersLast updated on May 26th, 2025
Factors of 2240
Factors of 2240 are numbers that can divide 2240 completely without leaving a remainder. We often use factors in activities like organizing events and seating arrangements in our daily lives. In this topic, we will learn more about the factors of 2240 and the different methods to find them.
What are the Factors of 2240
The factors of 2240 are the numbers that divide 2240 evenly.
The factors of 2240 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240.
Positive factors: These are negative counterparts of the positive factors.
Positive factors: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 40, 44, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240
Negative Factors: These are negative counterparts of the positive factors.
Negative factors: -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -32, -40, -44, -56, -64, -70, -80, -112, -140, -160, -224, -280, -320, -448, -560, -1120, -2240
Prime Factors and Prime Factorization
Prime factors are the prime numbers themselves, when multiplied together, give 2240 as the product. The prime factorization involves breaking 2240 into its prime factors. Prime factors of 2240: 2, 5, 7
Prime Factorization: Prime factorization involves expressing 2240 as the product of its prime factors.
Expressed as 26×51×71
Table of Factors of 2240
|
Positive Factors |
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240. |
|
Negative Factors |
-1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -28, -32, -35, -40, -56, -64, -70, -80, -112, -140, -160, -224, -280, -320, -448, -560, -1120, -2240 |
|
Prime Factors |
2, 5, 7 |
|
Prime Factorization |
26×51×71 |
This breakdown helps in understanding the various factors of 2240, whether they are positive or negative, as well as how prime factorization works for this number.
How to Find the Factors of 2240
There are different methods to find the factors of 2240:
Multiplication Method
Division Method
Prime Factor and Prime Factorization
Factor Tree
Finding Factors Using Multiplication Method
The multiplication method finds the pair of factors that give 2240 as their product.
Step 1: Find the pair of numbers whose product is 2240.
Step 2: The factors are those numbers, when multiplied, give 2240.
Step 3: Make a list of numbers whose product will be 2240.
A list of numbers whose products are 2240 is given below:
- 1 × 2240 = 2240
- 2 × 1120 = 2240
- 4 × 560 = 2240
- 5 × 448 = 2240
- 8 × 280 = 2240
- 10 × 224 = 2240
- 11 × 204 = 2240
- 16 × 140 = 2240
- 20 × 112 = 2240
- 22 × 102 = 2240
- 32 × 70 = 2240
- 40 × 56 = 2240
- 44 × 51 = 2240
Thus, the factors of 2240 are: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240.
Finding Factors Using Division Method
The division method finds the numbers that fully divide the given number. The steps are given below:
Step 1: Since every number is divisible by 1, 1 will always be a factor.
Example: 2240 ÷ 1 = 2240
Step 2: Move to the next integer. The factors of the number include the number that is used to divide and the number of times the particular number is divided.
Thus, the factors of 2240 are: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240.
Prime Factors and Prime Factorization
Multiplying prime numbers to get the given number as their product is called prime factors. A number, when simplified using the factors of that number, is expressed in the form of prime factors, which is known as prime factorization.
Prime Factors of 2240: Number 2240 has prime factors of 2, 5, and 7.
To find the prime factors of 2240:
Divide 2240 by 2 repeatedly until you get an odd number:
2240 ÷ 2 = 1120
1120 ÷ 2 = 560
560 ÷ 2 = 280
280 ÷ 2 = 140
140 ÷ 2 = 70
70 ÷ 2 = 35
Now, divide 35 by 5:
35 ÷ 5 = 7
Finally, divide 7 by 7:
7 ÷ 7 = 1
Prime Factorization of 2240: 26×51×71
Factor Tree
The prime factorization can be visually represented using a factor tree, which helps to understand the breakdown process easily.
Positive and Negative Factor Pairs of 2240
Factors of 2240 can be written in both positive pairs and negative pairs. They are like team members whose product will be equal to the given number.
Positive Factor Pairs: (1, 2240), (2, 1120), (4, 560), (5, 448), (8, 280), (10, 224), (11, 204), (16, 140), (20, 112), (22, 102), (32, 70), (40, 56), (44, 51)
Negative Factor Pairs: (-1, -2240), (-2, -1120), (-4, -560), (-5, -448), (-8, -280), (-10, -224), (-11, -204), (-16, -140), (-20, -112), (-22, -102), (-32, -70), (-40, -56), (-44, -51)
Common Mistakes and How to Avoid Them in Factors of 2240
Mistakes can occur while finding the factors. Here are some common errors and solutions:
Mistake 1
Assuming only prime numbers are factors.
Remember, all numbers that divide 2240 completely are factors, not just the prime numbers.
Factors of 2240 Examples
Problem 1
Can you check whether 48 and 32 are co-prime based on the factors of 2240?
No, 48 and 32 are not co-prime.
Explanation
To check whether the two numbers are co-prime, list their factors first. Once you have listed the factors, identify the common factors and determine the GCF. If the GCF is greater than 1, then the numbers are not co-prime.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 32: 1, 2, 4, 8, 16, 32
Here, the GCF is 16. So 48 and 32 are not co-prime. For co-prime, the GCF of numbers should be 1.
Problem 2
Verify whether 112 is a multiple of 16 using the factors of 2240.
Yes, 112 is a multiple of 16.
Explanation
Multiples of 16 are numbers we get when 16 is multiplied by another number. Since 16 × 7 = 112, 112 is a multiple of 16.
Problem 3
Identify the perfect square from the factors of 2240.
The perfect square factor of 2240 is 64 and the root is 8.
Explanation
A perfect square is a number we get when the same number is multiplied twice. When 8 is multiplied twice (8×8) we get the perfect square 64.
Problem 4
Determine if 2240 is divisible by 32.
Yes, 2240 is divisible by 32.
Explanation
To check divisibility, divide 2240 by 32 and check for a remainder. 2240 ÷ 32 = 70, which is an integer. Therefore, 2240 is divisible by 32.
Problem 5
What is the greatest common factor (GCF) of 2240 and 80?
The GCF of 2240 and 80 is 80.
Explanation
To find the GCF, list the factors of each number and choose the highest common factor.
Factors of 2240: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 64, 70, 80, 112, 140, 160, 224, 280, 320, 448, 560, 1120, 2240.
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
The highest common factor is 80.
FAQs on Factors of 2240
1.What are the factors of 2240?
2.How do you determine if a number is a factor of 2240?
3.What is the smallest factor of 2240?
4.What is the largest factor of 2240?
5.How many factors does 2240 have?
6.How many odd factors does 2240 have?
7.What factors go into 2240?
8.Do any perfect squares exist in the factors of 2240?
9.How can children in United Kingdom use numbers in everyday life to understand Factors of 2240?
10.What are some fun ways kids in United Kingdom can practice Factors of 2240 with numbers?
11.What role do numbers and Factors of 2240 play in helping children in United Kingdom develop problem-solving skills?
12.How can families in United Kingdom create number-rich environments to improve Factors of 2240 skills?
Important glossaries for the Factors of 2240
- Factors: Numbers that can divide a given number completely without leaving a remainder. Example: 1, 2, 4, 5, etc., are factors of 2240.
- Prime Factors: Prime numbers that, when multiplied together, result in the original number. Example: 2, 5, and 7 are the prime factors of 2240.
- Prime Factorization: The process of breaking down a number into its prime factors. Example: The prime factorization of 2240 is 26 × 51 × 71.
- Multiple: A number that is the product of a given number and an integer. Example: 112 is a multiple of 16 (since 16×7=112).
- Perfect Square: A number that is the product of an integer multiplied by itself. Example: 64 is a perfect square because 8×8=64.
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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.
Fun Fact
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