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102 LearnersLast updated on April 11th, 2025
Factors of 660
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 660, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 660?
The numbers that divide 660 evenly are known as factors of 660. A factor of 660 is a number that divides the number without remainder. The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, and 660.
Negative factors of 660: -1, -2, -3, -4, -5, -6, -10, -11, -12, -15, -20, -22, -30, -33, -44, -55, -60, -66, -110, -132, -165, -220, -330, and -660.
Prime factors of 660: 2, 3, 5, and 11.
Prime factorization of 660: 2 × 2 × 3 × 5 × 11.
The sum of factors of 660: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 11 + 12 + 15 + 20 + 22 + 30 + 33 + 44 + 55 + 60 + 66 + 110 + 132 + 165 + 220 + 330 + 660 = 2016
How to Find Factors of 660?
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 660. Identifying the numbers which are multiplied to get the number 660 is the multiplication method.
Step 1: Multiply 660 by 1, 660 × 1 = 660.
Step 2: Check for other numbers that give 660 after multiplying
2 × 330 = 660
3 × 220 = 660
4 × 165 = 660
5 × 132 = 660
6 × 110 = 660
10 × 66 = 660
11 × 60 = 660
12 × 55 = 660
15 × 44 = 660
20 × 33 = 660
22 × 30 = 660
Therefore, the positive factor pairs of 660 are: (1, 660), (2, 330), (3, 220), (4, 165), (5, 132), (6, 110), (10, 66), (11, 60), (12, 55), (15, 44), (20, 33), (22, 30). 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 the simple division method -
Step 1: Divide 660 by 1, 660 ÷ 1 = 660.
Step 2: Continue dividing 660 by the numbers until the remainder becomes 0.
660 ÷ 1 = 660
660 ÷ 2 = 330
660 ÷ 3 = 220
660 ÷ 4 = 165
660 ÷ 5 = 132
660 ÷ 6 = 110
660 ÷ 10 = 66
660 ÷ 11 = 60
660 ÷ 12 = 55
660 ÷ 15 = 44
660 ÷ 20 = 33
660 ÷ 22 = 30
Therefore, the factors of 660 are: 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660.
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 660 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
660 ÷ 2 = 330
330 ÷ 2 = 165
165 ÷ 3 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1
The prime factors of 660 are 2, 3, 5, and 11. The prime factorization of 660 is: 2 × 2 × 3 × 5 × 11.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 660 is divided by 2 to get 330.
Step 2: Now divide 330 by 2 to get 165.
Step 3: Then divide 165 by 3 to get 55.
Step 4: Divide 55 by 5 to get 11. Here, 11 is a prime number that cannot be divided anymore. So, the prime factorization of 660 is: 2 × 2 × 3 × 5 × 11.
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 660: (1, 660), (2, 330), (3, 220), (4, 165), (5, 132), (6, 110), (10, 66), (11, 60), (12, 55), (15, 44), (20, 33), (22, 30).
- Negative factor pairs of 660: (-1, -660), (-2, -330), (-3, -220), (-4, -165), (-5, -132), (-6, -110), (-10, -66), (-11, -60), (-12, -55), (-15, -44), (-20, -33), (-22, -30).
Common Mistakes and How to Avoid Them in Factors of 660
Factors of 660 Examples
Problem 1
There are 11 friends and 660 marbles. How will they divide it equally?
Explanation
Problem 2
A rectangular garden has a length of 15 meters and a total area of 660 square meters. Find the width.
Explanation
Problem 3
There are 6 boxes and 660 candies. How many candies will be in each box?
Explanation
Problem 4
In a theater, there are 660 seats, and 30 rows. How many seats are there in each row?
Explanation
Problem 5
660 books need to be arranged in 12 shelves. How many books will go on each shelf?
Explanation
FAQs on Factors of 660
1.What are the factors of 660?
2.Mention the prime factors of 660.
3.Is 660 a multiple of 4?
4.Mention the factor pairs of 660?
5.What is the square of 660?
Important Glossaries for Factor of 660
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, and 660.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 5, and 11 are prime factors of 660.
- 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 660 are (1, 660), (2, 330), etc.
- Prime factorization: The process of breaking down a number into its smallest prime components. For example, the prime factorization of 660 is 2 × 2 × 3 × 5 × 11.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 660 is a multiple of 4.
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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.
