105 LearnersLast updated on August 5th, 2025
GCF of 99 and 102
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 99 and 102.
What is the GCF of 99 and 102?
The greatest common factor of 99 and 102 is 3. The largest divisor of two or more numbers is called the GCF of the numbers. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1. The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 99 and 102?
To find the GCF of 99 and 102, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 99 and 102 by Using Listing of Factors
Steps to find the GCF of 99 and 102 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 99 = 1, 3, 9, 11, 33, 99.
Factors of 102 = 1, 2, 3, 6, 17, 34, 51, 102.
Step 2: Now, identify the common factors of them
Common factors of 99 and 102: 1, 3
Step 3: Choose the largest factor
The largest factor that both numbers have is 3.
The GCF of 99 and 102 is 3.
GCF of 99 and 102 Using Prime Factorization
To find the GCF of 99 and 102 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 99: 99 = 3 × 3 × 11 = 3² × 11
Prime Factors of 102: 102 = 2 × 3 × 17 = 2 × 3 × 17
Step 2: Now, identify the common prime factors
The common prime factor is: 3
Step 3: Multiply the common prime factors
3 = 3
The Greatest Common Factor of 99 and 102 is 3.
GCF of 99 and 102 Using Division Method or Euclidean Algorithm Method
To find the GCF of 99 and 102 using the Division Method or Euclidean Algorithm Method, follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 102 by 99
102 ÷ 99 = 1 (quotient), The remainder is calculated as 102 − (99 × 1) = 3
The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (99) by the previous remainder (3)
Divide 99 by 3
99 ÷ 3 = 33 (quotient), remainder = 99 − (3 × 33) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 99 and 102 is 3.
Common Mistakes and How to Avoid Them in GCF of 99 and 102
Finding the GCF of 99 and 102 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 99, students may mention 5, which is incorrect.
To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the Wrong Common Factor
Students may sometimes select the smallest common factor instead of the largest one.
To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to Include 1 as a Factor
Sometimes students may forget 1 as a common factor of the numbers.
However, it does not affect the GCF, but it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors and multiples. In that confusion, sometimes they may write multiples instead of factors.
To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is Always an Even Number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number.
To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 99 and 102 Examples
Problem 1
A chef has 99 apples and 102 oranges. She wants to pack them into equal-sized boxes with the largest number of fruits in each box. How many fruits will be in each box?
We should find the GCF of 99 and 102
GCF of 99 and 102 = 3
There are 3 equal groups
99 ÷ 3 = 33
102 ÷ 3 = 34
There will be 3 boxes, and each box gets 33 apples and 34 oranges.
Explanation
As the GCF of 99 and 102 is 3, the chef can make 3 boxes.
Now divide 99 and 102 by 3.
Each box gets 33 apples and 34 oranges.
Problem 2
A farmer has 99 rows of corn and 102 rows of wheat. He wants to organize them into sections, with the same number of rows in each section, using the largest possible number of rows per section. How many rows will be in each section?
GCF of 99 and 102 = 3
So each section will have 3 rows.
Explanation
There are 99 rows of corn and 102 rows of wheat.
To find the total number of rows in each section, we should find the GCF of 99 and 102.
There will be 3 rows in each section.
Problem 3
A tailor has a 99-meter roll of red fabric and a 102-meter roll of blue fabric. She wants to cut both rolls into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 99 and 102
The GCF of 99 and 102 = 3
The fabric is 3 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 99 and 102, which is 3.
The length of each piece of the fabric will be 3 meters.
Problem 4
A carpenter has two wooden planks, one 99 cm long and the other 102 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood
GCF of 99 and 102 = 3
The longest length of each piece is 3 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 99 cm and 102 cm, respectively, we have to find the GCF of 99 and 102, which is 3 cm.
The longest length of each piece is 3 cm.
Problem 5
If the GCF of 99 and ‘b’ is 3, and the LCM is 3366, find ‘b’.
The value of ‘b’ is 102.
Explanation
GCF × LCM = product of the numbers
3 × 3366 = 99 × b
10098 = 99b
b = 10098 ÷ 99 = 102
FAQs on the Greatest Common Factor of 99 and 102
1.What is the LCM of 99 and 102?
2.Is 99 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 102?
5.Are 99 and 102 prime numbers?
6.How can children in Saudi Arabia use numbers in everyday life to understand GCF of 99 and 102?
7.What are some fun ways kids in Saudi Arabia can practice GCF of 99 and 102 with numbers?
8.What role do numbers and GCF of 99 and 102 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve GCF of 99 and 102 skills?
Important Glossaries for GCF of 99 and 102
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.
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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.
