126 LearnersLast updated on May 26th, 2025
Factors of 7000
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 7000, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 7000?
The numbers that divide 7000 evenly are known as factors of 7000.
A factor of 7000 is a number that divides the number without remainder.
The factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, and 7000.
Negative factors of 7000: -1, -2, -4, -5, -7, -8, -10, -14, -20, -25, -28, -35, -40, -50, -56, -70, -100, -125, -140, -175, -200, -250, -280, -350, -500, -700, -875, -1000, -1400, -1750, -3500, and -7000.
Prime factors of 7000: 2, 5, and 7.
Prime factorization of 7000: 2³ × 5³ × 7.
The sum of factors of 7000: 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 20 + 25 + 28 + 35 + 40 + 50 + 56 + 70 + 100 + 125 + 140 + 175 + 200 + 250 + 280 + 350 + 500 + 700 + 875 + 1000 + 1400 + 1750 + 3500 + 7000 = 20176
How to Find Factors of 7000?
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 7000. Identifying the numbers which are multiplied to get the number 7000 is the multiplication method.
Step 1: Multiply 7000 by 1, 7000 × 1 = 7000.
Step 2: Check for other numbers that give 7000 after multiplying
2 × 3500 = 7000
4 × 1750 = 7000
5 × 1400 = 7000
7 × 1000 = 7000
8 × 875 = 7000
10 × 700 = 7000
14 × 500 = 7000
20 × 350 = 7000
25 × 280 = 7000
28 × 250 = 7000
35 × 200 = 7000
40 × 175 = 7000
50 × 140 = 7000
56 × 125 = 7000
70 × 100 = 7000
Therefore, the positive factor pairs of 7000 are: (1, 7000), (2, 3500), (4, 1750), (5, 1400), (7, 1000), (8, 875), (10, 700), (14, 500), (20, 350), (25, 280), (28, 250), (35, 200), (40, 175), (50, 140), (56, 125), (70, 100).
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 7000 by 1, 7000 ÷ 1 = 7000.
Step 2: Continue dividing 7000 by the numbers until the remainder becomes 0.
7000 ÷ 1 = 7000
7000 ÷ 2 = 3500
7000 ÷ 4 = 1750
7000 ÷ 5 = 1400
7000 ÷ 7 = 1000
7000 ÷ 8 = 875
7000 ÷ 10 = 700
7000 ÷ 14 = 500
7000 ÷ 20 = 350
7000 ÷ 25 = 280
7000 ÷ 28 = 250
7000 ÷ 35 = 200
7000 ÷ 40 = 175
7000 ÷ 50 = 140
7000 ÷ 56 = 125
7000 ÷ 70 = 100
Therefore, the factors of 7000 are: 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, and 7000.
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 7000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
7000 ÷ 2 = 3500
3500 ÷ 2 = 1750
1750 ÷ 2 = 875
875 ÷ 5 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 7000 are 2, 5, and 7.
The prime factorization of 7000 is: 2³ × 5³ × 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, 7000 is divided by 2 to get 3500.
Step 2: Now divide 3500 by 2 to get 1750.
Step 3: Then divide 1750 by 2 to get 875.
Step 4: Divide 875 by 5 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 7000 is: 2³ × 5³ × 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 7000: (1, 7000), (2, 3500), (4, 1750), (5, 1400), (7, 1000), (8, 875), (10, 700), (14, 500), (20, 350), (25, 280), (28, 250), (35, 200), (40, 175), (50, 140), (56, 125), (70, 100).
Negative factor pairs of 7000: (-1, -7000), (-2, -3500), (-4, -1750), (-5, -1400), (-7, -1000), (-8, -875), (-10, -700), (-14, -500), (-20, -350), (-25, -280), (-28, -250), (-35, -200), (-40, -175), (-50, -140), (-56, -125), (-70, -100).
Common Mistakes and How to Avoid Them in Factors of 7000
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 7000, 1 and 7000 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 7000 consist of -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 7000/1.5 = 4666.67, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 7000 are prime numbers.
For example, 2, 5, and 7 are the prime factors of 7000, but it has other factors like 4, 10, 14, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 7000 as 2³ × 5³ × 7 and missing all the key factors.
Factors of 7000 Examples
Problem 1
A group of 14 people wants to buy 7000 candies for a festival. How many candies will each person get if they are divided equally?
They will get 500 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of people.
7000/14 = 500
Problem 2
A rectangular garden has a length of 100 meters, and the total area is 7000 square meters. What is the width?
70 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
7000 = 100 × width
To find the value of the width, we need to shift 100 to the left side.
7000/100 = width
Width = 70.
Problem 3
There are 28 trucks and 7000 packages. How many packages will be in each truck?
Each truck will have 250 packages.
Explanation
To find the packages in each truck, divide the total packages by the number of trucks.
7000/28 = 250
Problem 4
A company has 7000 documents and 25 filing cabinets. How many documents can each cabinet hold?
Each cabinet can hold 280 documents.
Explanation
Dividing the documents by the total cabinets, we will get the number of documents in each cabinet.
7000/25 = 280
Problem 5
A library has 7000 books and 35 shelves. How many books will go on each shelf?
Each of the shelves has 200 books.
Explanation
Divide total books by shelves.
7000/35 = 200
FAQs on Factors of 7000
1.What are the factors of 7000?
2.Mention the prime factors of 7000.
3.Is 7000 a multiple of 5?
4.Mention the factor pairs of 7000?
5.What is the cube of 7000?
6.How can children in Australia use numbers in everyday life to understand Factors of 7000?
7.What are some fun ways kids in Australia can practice Factors of 7000 with numbers?
8.What role do numbers and Factors of 7000 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 7000 skills?
Important Glossaries for Factors of 7000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, and 7000.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 7000.
- 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 7000 are (1, 7000), (2, 3500), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 7000 is 2³ × 5³ × 7.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find factor pairs of 7000 such as (10, 700).
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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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