101 LearnersLast updated on May 26th, 2025
Factors of 668
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 668, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 668?
The numbers that divide 668 evenly are known as factors of 668.
A factor of 668 is a number that divides the number without remainder.
The factors of 668 are 1, 2, 4, 167, 334, and 668.
Negative factors of 668: -1, -2, -4, -167, -334, and -668.
Prime factors of 668: 2 and 167.
Prime factorization of 668: 2² × 167.
The sum of factors of 668: 1 + 2 + 4 + 167 + 334 + 668 = 1176
How to Find Factors of 668?
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 668. Identifying the numbers which are multiplied to get the number 668 is the multiplication method.
Step 1: Multiply 668 by 1, 668 × 1 = 668.
Step 2: Check for other numbers that give 668 after multiplying
2 × 334 = 668
4 × 167 = 668
Therefore, the positive factor pairs of 668 are: (1, 668), (2, 334), and (4, 167).
All these factor pairs result in 668.
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 668 by 1, 668 ÷ 1 = 668.
Step 2: Continue dividing 668 by the numbers until the remainder becomes 0.
668 ÷ 1 = 668
668 ÷ 2 = 334
668 ÷ 4 = 167
Therefore, the factors of 668 are: 1, 2, 4, 167, 334, 668.
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 668 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
668 ÷ 2 = 334
334 ÷ 2 = 167
167 ÷ 167 = 1
The prime factors of 668 are 2 and 167.
The prime factorization of 668 is: 2² × 167.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 668 is divided by 2 to get 334.
Step 2: Now divide 334 by 2 to get 167.
Step 3: Since 167 is a prime number, it cannot be divided further. So, the prime factorization of 668 is: 2² × 167.
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 668: (1, 668), (2, 334), and (4, 167).
Negative factor pairs of 668: (-1, -668), (-2, -334), and (-4, -167).
Common Mistakes and How to Avoid Them in Factors of 668
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
People 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 668, 1 and 668 are also factors.
Factors of 668 Examples
Problem 1
A group of 4 people receives 668 marbles to share equally. How many marbles will each person receive?
Each person will receive 167 marbles.
Explanation
To divide the marbles equally, we need to divide the total marbles by the number of people.
668/4 = 167
Problem 2
A rectangular field has a width of 2 meters and a total area of 668 square meters. Find the length of the field.
334 meters.
Explanation
To find the length of the field, we use the formula, Area = length × width 668 = length × 2
To find the value of length, divide 668 by 2.
668/2 = length
Length = 334.
Problem 3
There are 334 gift bags and 668 candies. How many candies will be in each gift bag?
Each gift bag will have 2 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags. 668/334 = 2
Problem 4
In a classroom, there are 668 chairs arranged in 167 rows. How many chairs are in each row?
There are 4 chairs in each row.
Explanation
Dividing the chairs by the total rows, we will get the number of chairs in each row.
668/167 = 4
Problem 5
668 books need to be arranged in 2 shelves. How many books will go on each shelf?
Each of the shelves has 334 books.
Explanation
Divide total books by shelves.
668/2 = 334
FAQs on Factors of 668
1.What are the factors of 668?
2.Mention the prime factors of 668.
3.Is 668 a multiple of 4?
4.Mention the factor pairs of 668?
5.What is the square of 668?
Important Glossaries for Factors of 668
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 668 are 1, 2, 4, 167, 334, and 668.
- Prime factors: The factors which are prime numbers. For example, 2 and 167 are prime factors of 668.
- 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 668 are (1, 668), (2, 334), and (4, 167).
- Prime factorization: The process of expressing a number as the product of its prime factors. For instance, the prime factorization of 668 is 2² × 167.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
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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.
