122 LearnersLast updated on May 26th, 2025
Factors of 2800
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 2800, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2800?
The numbers that divide 2800 evenly are known as factors of 2800.
A factor of 2800 is a number that divides the number without remainder.
The factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, and 2800.
Negative factors of 2800: -1, -2, -4, -5, -7, -8, -10, -14, -16, -20, -25, -28, -35, -40, -50, -56, -70, -80, -100, -112, -140, -175, -200, -280, -350, -400, -560, -700, -1400, and -2800.
Prime factors of 2800: 2, 5, and 7.
Prime factorization of 2800: (24 times 52 times 7).
The sum of factors of 2800: 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 16 + 20 + 25 + 28 + 35 + 40 + 50 + 56 + 70 + 80 + 100 + 112 + 140 + 175 + 200 + 280 + 350 + 400 + 560 + 700 + 1400 + 2800 = 8190
How to Find Factors of 2800?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 2800. Identifying the numbers which are multiplied to get the number 2800 is the multiplication method.
Step 1: Multiply 2800 by 1, 2800 × 1 = 2800.
Step 2: Check for other numbers that give 2800 after multiplying:
2 × 1400 = 2800
4 × 700 = 2800
5 × 560 = 2800
7 × 400 = 2800
8 × 350 = 2800
10 × 280 = 2800
14 × 200 = 2800
16 × 175 = 2800
20 × 140 = 2800
25 × 112 = 2800
28 × 100 = 2800
35 × 80 = 2800
40 × 70 = 2800
50 × 56 = 2800
Therefore, the positive factor pairs of 2800 are: (1, 2800), (2, 1400), (4, 700), (5, 560), (7, 400), (8, 350), (10, 280), (14, 200), (16, 175), (20, 140), (25, 112), (28, 100), (35, 80), (40, 70), (50, 56). 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 in whole numbers as factors. Factors can be calculated by following a simple division method:
Step 1: Divide 2800 by 1, 2800 ÷ 1 = 2800.
Step 2: Continue dividing 2800 by the numbers until the remainder becomes 0.
2800 ÷ 1 = 2800
2800 ÷ 2 = 1400
2800 ÷ 4 = 700
2800 ÷ 5 = 560
2800 ÷ 7 = 400
2800 ÷ 8 = 350
2800 ÷ 10 = 280
2800 ÷ 14 = 200
2800 ÷ 16 = 175
2800 ÷ 20 = 140
2800 ÷ 25 = 112
2800 ÷ 28 = 100
2800 ÷ 35 = 80
2800 ÷ 40 = 70
2800 ÷ 50 = 56
Therefore, the factors of 2800 are: 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, 2800.
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 2800 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2800 ÷ 2 = 1400
1400 ÷ 2 = 700
700 ÷ 2 = 350
350 ÷ 2 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 2800 are 2, 5, and 7.
The prime factorization of 2800 is: (24 times 52 times 7).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2800 is divided by 2 to get 1400.
Step 2: Now divide 1400 by 2 to get 700.
Step 3: Then divide 700 by 2 to get 350.
Step 4: Divide 350 by 2 to get 175.
Step 5: Divide 175 by 5 to get 35.
Step 6: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 2800 is: (24 times 52 times 7).
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 2800: (1, 2800), (2, 1400), (4, 700), (5, 560), (7, 400), (8, 350), (10, 280), (14, 200), (16, 175), (20, 140), (25, 112), (28, 100), (35, 80), (40, 70), (50, 56).
Negative factor pairs of 2800: (-1, -2800), (-2, -1400), (-4, -700), (-5, -560), (-7, -400), (-8, -350), (-10, -280), (-14, -200), (-16, -175), (-20, -140), (-25, -112), (-28, -100), (-35, -80), (-40, -70), (-50, -56).
Common Mistakes and How to Avoid Them in Factors of 2800
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and 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 2800, 1 and 2800 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 2800 include -1, -2, -4, etc.
Mistake 3
Including Fractions
Children might sometimes mistakenly consider fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor, because 2800/1.5 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 2800 are prime numbers. While 2, 5, and 7 are the prime factors of 2800, it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip steps in factorization and end up writing wrong factors.
For example, not breaking 2800 as (24 times 52 times 7) and missing key factors.
Factors of 2800 Examples
Problem 1
There are 14 friends and 2800 apples. How will they divide them equally?
They will get 200 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of friends.
2800/14 = 200
Problem 2
A garden is rectangular, the length of the garden is 40 meters and the total area is 2800 square meters. Find the width.
70 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2800 = 40 × width
To find the value of width, we need to shift 40 to the left side.
2800/40 = width
Width = 70.
Problem 3
There are 56 bags and 2800 candies. How many candies will be in each bag?
Each bag will have 50 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
2800/56 = 50
Problem 4
In a class, there are 2800 students, and 100 groups. How many students are there in each group?
There are 28 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
2800/100 = 28
Problem 5
2800 books need to be arranged in 400 shelves. How many books will go on each shelf?
Each of the shelves has 7 books.
Explanation
Divide total books by shelves.
2800/400 = 7
FAQs on Factors of 2800
1.What are the factors of 2800?
2.Mention the prime factors of 2800.
3.Is 2800 a multiple of 10?
4.Mention the factor pairs of 2800?
5.What is the square of 2800?
6.How can children in Oman use numbers in everyday life to understand Factors of 2800?
7.What are some fun ways kids in Oman can practice Factors of 2800 with numbers?
8.What role do numbers and Factors of 2800 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve Factors of 2800 skills?
Important Glossaries for Factors of 2800
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2800 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 50, 56, 70, 80, 100, 112, 140, 175, 200, 280, 350, 400, 560, 700, 1400, and 2800.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 2800.
- 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 2800 are (1, 2800), (2, 1400), etc.
- Prime factorization: Breaking down a number into its prime factors. For instance, the prime factorization of 2800 is \(24 times 52 times 7).
- Multiples: Numbers that can be divided by another number without a remainder. For example, 2800 is a multiple of 10.
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About BrightChamps in Oman
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
: She loves to read number jokes and games.
