107 LearnersLast updated on May 26th, 2025
Factors of 102
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 102, how they are used in real life, and tips to learn them quickly.
What are the Factors of 102?
The numbers that divide 102 evenly are known as factors of 102. A factor of 102 is a number that divides the number without remainder. The factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.
Negative factors of 102: -1, -2, -3, -6, -17, -34, -51, and -102.
Prime factors of 102: 2, 3, and 17.
Prime factorization of 102: 2 × 3 × 17.
The sum of factors of 102: 1 + 2 + 3 + 6 + 17 + 34 + 51 + 102 = 216
How to Find Factors of 102?
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 102. Identifying the numbers which are multiplied to get the number 102 is the multiplication method.
Step 1: Multiply 102 by 1, 102 × 1 = 102.
Step 2: Check for other numbers that give 102 after multiplying 2 × 51 = 102
3 × 34 = 102
6 × 17 = 102
Therefore, the positive factor pairs of 102 are: (1, 102), (2, 51), (3, 34), and (6, 17). 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 102 by 1, 102 ÷ 1 = 102.
Step 2: Continue dividing 102 by the numbers until the remainder becomes 0.
102 ÷ 1 = 102
102 ÷ 2 = 51
102 ÷ 3 = 34
102 ÷ 6 = 17
Therefore, the factors of 102 are: 1, 2, 3, 6, 17, 34, 51, 102.
Prime Factors and Prime Factorization
The factors can be found by dividing it 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 102 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
102 ÷ 2 = 51
51 ÷ 3 = 17
17 ÷ 17 = 1
The prime factors of 102 are 2, 3, and 17. The prime factorization of 102 is: 2 × 3 × 17.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 102 is divided by 2 to get 51.
Step 2: Now divide 51 by 3 to get 17.
Step 3: Here, 17 is a prime number and cannot be divided anymore. So, the prime factorization of 102 is: 2 × 3 × 17.
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 102: (1, 102), (2, 51), (3, 34), and (6, 17).
- Negative factor pairs of 102: (-1, -102), (-2, -51), (-3, -34), and (-6, -17).
Common Mistakes and How to Avoid Them in Factors of 102
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 102, 1 and 102 are also factors.
Factors of 102 Examples
Problem 1
There are 102 apples to be packed equally into boxes. If each box can hold 17 apples, how many boxes will be needed?
6 boxes will be needed.
Explanation
To pack the apples equally, divide the total apples by the number of apples each box can hold.
102/17 = 6
Problem 2
A garden is rectangular, the length of the garden is 34 meters, and the total area is 102 square meters. Find the width.
3 meters.
Explanation
To find the width of the garden, use the formula,
Area = length × width
102 = 34 × width
To find the value of width, shift 34 to the left side.
102/34 = width
Width = 3.
Problem 3
There are 51 students and 102 chairs. How many chairs will each student get if they are distributed equally?
Each student will get 2 chairs.
Explanation
To find the chairs each student will get, divide the total chairs by the number of students.
102/51 = 2
Problem 4
In a class, there are 102 students, and 6 groups. How many students are there in each group?
There are 17 students in each group.
Explanation
Dividing the students by the total groups, we get the number of students in each group. 102/6 = 17
Problem 5
102 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each shelf will have 34 books.
Explanation
Divide total books by shelves. 102/3 = 34
FAQs on Factors of 102
1.What are the factors of 102?
2.Mention the prime factors of 102.
3.Is 102 a multiple of 3?
4.Mention the factor pairs of 102.
5.What is the cube of 102?
Important Glossaries for Factors of 102
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 17 are prime factors of 102.
- 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 102 are (1, 102), (2, 51), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 102 is 2 × 3 × 17.
- Negative factors: Factors that are negative integers. For example, -1, -2, -3, etc., are negative factors of 102.
Explore More numbers
Previous to Factors of 102
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.
