132 LearnersLast updated on May 26th, 2025
Factors of 700
Factors are the numbers that divide any given number evenly without a 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 700, how they are used in real life, and tips to learn them quickly.
What are the Factors of 700?
The numbers that divide 700 evenly are known as factors of 700.
A factor of 700 is a number that divides the number without a remainder.
The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700.
Negative factors of 700: -1, -2, -4, -5, -7, -10, -14, -20, -25, -28, -35, -50, -70, -100, -140, -175, -350, and -700.
Prime factors of 700: 2, 5, and 7.
Prime factorization of 700: 2² × 5² × 7.
The sum of factors of 700: 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 25 + 28 + 35 + 50 + 70 + 100 + 140 + 175 + 350 + 700 = 1646
How to Find Factors of 700?
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 700. Identifying the numbers which are multiplied to get the number 700 is the multiplication method.
Step 1: Multiply 700 by 1, 700 × 1 = 700.
Step 2: Check for other numbers that give 700 after multiplying
2 × 350 = 700
4 × 175 = 700
5 × 140 = 700
7 × 100 = 700
10 × 70 = 700
14 × 50 = 700
20 × 35 = 700
Therefore, the positive factor pairs of 700 are: (1, 700), (2, 350), (4, 175), (5, 140), (7, 100), (10, 70), (14, 50), (20, 35).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Divide the given number with whole numbers until the remainder becomes zero and list out the numbers which result as whole numbers as factors. Factors can be calculated by following this simple division method
Step 1: Divide 700 by 1, 700 ÷ 1 = 700.
Step 2: Continue dividing 700 by the numbers until the remainder becomes 0.
700 ÷ 1 = 700
700 ÷ 2 = 350
700 ÷ 4 = 175
700 ÷ 5 = 140
700 ÷ 7 = 100
700 ÷ 10 = 70
700 ÷ 14 = 50
700 ÷ 20 = 35
Therefore, the factors of 700 are: 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700.
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 700 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
700 ÷ 2 = 350
350 ÷ 2 = 175
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
The prime factors of 700 are 2, 5, and 7.
The prime factorization of 700 is: 2² × 5² × 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, 700 is divided by 2 to get 350.
Step 2: Now divide 350 by 2 to get 175.
Step 3: Then divide 175 by 5 to get 35.
Step 4: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 700 is: 2² × 5² × 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 700: (1, 700), (2, 350), (4, 175), (5, 140), (7, 100), (10, 70), (14, 50), (20, 35).
Negative factor pairs of 700: (-1, -700), (-2, -350), (-4, -175), (-5, -140), (-7, -100), (-10, -70), (-14, -50), (-20, -35).
Common Mistakes and How to Avoid Them in Factors of 700
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 700, 1 and 700 are also factors.
Mistake 2
Missing Negative Factors
We tend to mention only positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 700 include -1, -2, -4, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 700/1.5 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 700 are prime numbers.
For example, 2, 5, and 7 are the prime factors of 700, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 700 as 2² × 5² × 7 and missing all the key factors.
Factors of 700 Examples
Problem 1
There are 7 teams, and a total of 700 points are scored in a tournament. How many points will each team have if they are distributed equally?
Each team will have 100 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of teams.
700/7 = 100
Problem 2
A rectangular garden has a length of 50 meters and a total area of 700 square meters. Find the width of the garden.
14 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
700 = 50 × width
To find the value of width, we need to shift 50 to the left side.
700/50 = width
Width = 14.
Problem 3
There are 25 bags and 700 apples. How many apples will be in each bag?
Each bag will have 28 apples.
Explanation
To find the apples in each bag, divide the total apples by the bags.
700/25 = 28
Problem 4
In a class, there are 35 students, and they collectively have 700 pencils. How many pencils does each student have?
Each student has 20 pencils.
Explanation
Dividing the pencils by the total number of students, we will get the number of pencils each student has.
700/35 = 20
Problem 5
700 books need to be arranged in 10 shelves. How many books will go on each shelf?
Each of the shelves has 70 books.
Explanation
Divide total books by shelves.
700/10 = 70
FAQs on Factors of 700
1.What are the factors of 700?
2.Mention the prime factors of 700.
3.Is 700 a multiple of 10?
4.Mention the factor pairs of 700?
5.What is the square of 700?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 700?
7.What are some fun ways kids in United Kingdom can practice Factors of 700 with numbers?
8.What role do numbers and Factors of 700 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 700 skills?
Important Glossaries for Factor of 700
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, and 700.
- Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 700.
- 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 700 are (1, 700), (2, 350), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 700 is 2² × 5² × 7.
- Multiples: Numbers that are the product of a number and any integer. For example, 700 is a multiple of 10.
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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
: She loves to read number jokes and games.
