106 LearnersLast updated on May 26th, 2025
Factors of 167
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 167, how they are used in real life, and tips to learn them quickly.
What are the Factors of 167?
The numbers that divide 167 evenly are known as factors of 167. A factor of 167 is a number that divides the number without a remainder. Since 167 is a prime number, it has only two factors: 1 and 167.
Negative factors of 167: -1 and -167.
Prime factor of 167: 167 itself.
Prime factorization of 167: 167.
The sum of factors of 167: 1 + 167 = 168
How to Find Factors of 167?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 167. Since 167 is a prime number, it can only be expressed as:
Step 1: Multiply 167 by 1, 167 × 1 = 167.
Therefore, the only positive factor pair of 167 is: (1, 167). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 a simple division method -
Step 1: Divide 167 by 1, 167 ÷ 1 = 167.
Step 2: Check for other numbers until the remainder becomes 0, but since 167 is prime, no other division yields a whole number. Therefore, the factors of 167 are: 1 and 167.
Prime Factors and Prime Factorization
The factors can be found by dividing with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: Since 167 is a prime number, it cannot be broken down further. The prime factor of 167 is 167 itself. The prime factorization of 167 is: 167.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. For 167, which is a prime number, it cannot be broken down further. It stands alone as 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 167: (1, 167).
- Negative factor pairs of 167: (-1, -167).
Common Mistakes and How to Avoid Them in Factors of 167
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 include the given number itself and 1 as factors. The number itself and 1 are factors for every number. Always remember to include 1 and the number itself. For example, in factors of 167, 1 and 167 are also factors.
Factors of 167 Examples
Problem 1
A library has 167 books and wants to arrange them on shelves with an equal number of books. What are the possible arrangements?
The library can arrange 1 book per shelf on 167 shelves, or all 167 books on 1 shelf.
Explanation
Since 167 is a prime number, it only allows for arrangements of 1 book per shelf or all books on one shelf:
167 ÷ 1 = 167
167 ÷ 167 = 1
Problem 2
A group has 167 students, and they want to form teams such that each team has an equal number of students. How many ways can they form such teams?
They can form 1 team of 167 students or 167 teams of 1 student each.
Explanation
With 167 being a prime number, the only ways to divide evenly are:
167 ÷ 1 = 167
167 ÷ 167 = 1
Problem 3
A farmer has 167 apples and wants to distribute them equally among baskets. How many baskets can he use?
The farmer can use 1 basket with all apples or 167 baskets with 1 apple each.
Explanation
The only factor pairs of 167 are:
167 ÷ 1 = 167
167 ÷ 167 = 1
Problem 4
A company has 167 employees and plans to organize them into equal groups for a project. How can they group them?
They can form 1 group of 167 employees or 167 groups of 1 employee each.
Explanation
Since 167 is a prime number, it can only be divided as:
167 ÷ 1 = 167
167 ÷ 167 = 1
Problem 5
167 chairs need to be arranged in a conference room. What are the possible arrangements?
The chairs can be arranged in 1 row of 167 chairs or 167 rows of 1 chair each.
Explanation
The only factor pairs of 167 are:
167 ÷ 1 = 167
167 ÷ 167 = 1
FAQs on Factors of 167
1.What are the factors of 167?
2.Is 167 a prime number?
3.What is the prime factorization of 167?
4.Can 167 be divided by any number other than 1 and itself without a remainder?
5.What are the factor pairs of 167?
Important Glossaries for Factors of 167
- Factors: Numbers that divide the given number without leaving a remainder. For example, the factors of 167 are 1 and 167.
- Prime number: A number greater than 1 that has no divisors other than 1 and itself. For example, 167 is a prime number.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 167 is 167.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number. For example, the factor pairs of 167 are (1, 167).
- Negative factors: Factors that are negative counterparts of positive factors. For example, the negative factors of 167 are -1 and -167.
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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.
