101 LearnersLast updated on May 26th, 2025
Factors of 667
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 667, how they are used in real life, and tips to learn them quickly.
What are the Factors of 667?
The numbers that divide 667 evenly are known as factors of 667.
A factor of 667 is a number that divides the number without remainder.
The factors of 667 are 1, 23, 29, and 667.
Negative factors of 667: -1, -23, -29, and -667.
Prime factors of 667: 23 and 29.
Prime factorization of 667: 23 × 29.
The sum of factors of 667: 1 + 23 + 29 + 667 = 720
How to Find Factors of 667?
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 667. Identifying the numbers which are multiplied to get the number 667 is the multiplication method.
Step 1: Multiply 667 by 1, 667 × 1 = 667.
Step 2: Check for other numbers that give 667 after multiplying
23 × 29 = 667
Therefore, the positive factor pairs of 667 are: (1, 667) and (23, 29).
All these factor pairs result in 667.
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 in whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 667 by 1, 667 ÷ 1 = 667.
Step 2: Continue dividing 667 by the numbers until the remainder becomes 0.
667 ÷ 1 = 667
667 ÷ 23 = 29
667 ÷ 29 = 23
Therefore, the factors of 667 are: 1, 23, 29, 667.
Prime Factors and Prime Factorization
The factors can be found by dividing them with a prime number. 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 667 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
667 ÷ 23 = 29
29 ÷ 29 = 1
The prime factors of 667 are 23 and 29.
The prime factorization of 667 is: 23 × 29.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 667 is divided by 23 to get 29.
Step 2: Now divide 29 by 29 to get 1. Here, both 23 and 29 are the smallest prime numbers, that cannot be divided anymore. So, the prime factorization of 667 is: 23 × 29.
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 667: (1, 667) and (23, 29).
Negative factor pairs of 667: (-1, -667) and (-23, -29).
Common Mistakes and How to Avoid Them in Factors of 667
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 667, 1 and 667 are also factors.
Factors of 667 Examples
Problem 1
There are 29 trucks and 667 boxes. How will they load them equally?
They will load 23 boxes in each truck.
Explanation
To load the boxes equally, we need to divide the total boxes by the number of trucks.
667/29 = 23
Problem 2
A garden is rectangular, the length of the garden is 23 meters and the total area is 667 square meters. Find the width?
29 meters.
Explanation
To find the width of the garden, we use the formula, Area = length × width 667 = 23 × width
To find the value of width, we need to shift 23 to the left side.
667/23 = width
Width = 29.
Problem 3
There are 23 baskets and 667 apples. How many apples will be in each basket?
Each basket will have 29 apples.
Explanation
To find the apples in each basket, divide the total apples by the number of baskets.
667/23 = 29
Problem 4
In a class, there are 667 students, and 23 groups. How many students are there in each group?
There are 29 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
667/23 = 29
Problem 5
667 books need to be arranged in 23 shelves. How many books will go on each shelf?
Each of the shelves has 29 books.
Explanation
Divide total books by shelves.
667/23 = 29
FAQs on Factors of 667
1.What are the factors of 667?
2.Mention the prime factors of 667.
3.Is 667, a multiple of 23?
4.Mention the factor pairs of 667?
5.What is the square of 667?
Important Glossaries for Factor of 667
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 667 are 1, 23, 29, and 667.
- Prime factors: The factors which are prime numbers. For example, 23 and 29 are prime factors of 667.
- 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 667 are (1, 667) and (23, 29).
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 667 is 23 × 29.
- Negative factors: Factors that are negative counterparts of the positive factors. For example, the negative factors of 667 are -1, -23, -29, and -667.
Explore More numbers
Previous to Factors of 667
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.
