Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To distribute the points equally, we need to divide the total points by the number of teams.
700/7 = 100
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.
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.
There are 25 bags and 700 apples. How many apples will be in each bag?
Each bag will have 28 apples.
To find the apples in each bag, divide the total apples by the bags.
700/25 = 28
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.
Dividing the pencils by the total number of students, we will get the number of pencils each student has.
700/35 = 20
700 books need to be arranged in 10 shelves. How many books will go on each shelf?
Each of the shelves has 70 books.
Divide total books by shelves.
700/10 = 70
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.
: She loves to read number jokes and games.