100 LearnersLast updated on August 5th, 2025
GCF of 65 and 100
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 65 and 100.
What is the GCF of 65 and 100?
The greatest common factor of 65 and 100 is 5. The largest divisor of two or more numbers is called the GCF of the number.
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 65 and 100?
To find the GCF of 65 and 100, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 65 and 100 by Using Listing of Factors
Steps to find the GCF of 65 and 100 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 65 = 1, 5, 13, 65.
Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100.
Step 2: Now, identify the common factors of them
Common factors of 65 and 100: 1, 5.
Step 3: Choose the largest factor
The largest factor that both numbers have is 5.
The GCF of 65 and 100 is 5.
GCF of 65 and 100 Using Prime Factorization
To find the GCF of 65 and 100 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 65: 65 = 5 × 13
Prime Factors of 100: 100 = 2 × 2 × 5 × 5 = 2² × 5²
Step 2: Now, identify the common prime factors
The common prime factor is 5.
Step 3: Multiply the common prime factors
The Greatest Common Factor of 65 and 100 is 5.
GCF of 65 and 100 Using Division Method or Euclidean Algorithm Method
Find the GCF of 65 and 100 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 100 by 65 100 ÷ 65 = 1 (quotient)
The remainder is calculated as 100 - (65×1) = 35
The remainder is 35, not zero, so continue the process
Step 2: Now divide the previous divisor (65) by the previous remainder (35)
Divide 65 by 35 65 ÷ 35 = 1 (quotient), remainder = 65 - (35×1) = 30
The remainder is 30, not zero, so continue the process
Step 3: Now divide the previous divisor (35) by the previous remainder (30)
Divide 35 by 30 35 ÷ 30 = 1 (quotient), remainder = 35 - (30×1) = 5
The remainder is 5, which is not zero, so continue the process
Step 4: Now divide the previous divisor (30) by the remainder (5)
Divide 30 by 5 30 ÷ 5 = 6 (quotient), remainder = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 65 and 100 is 5.
Common Mistakes and How to Avoid Them in GCF of 65 and 100
Finding GCF of 65 and 100 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 65, students may mention 10 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 tells about incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between 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 that 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 65 and 100 Examples
Problem 1
A gardener has 65 rose plants and 100 sunflower plants. She wants to arrange them in rows with the largest possible number of plants in each row. How many plants will be in each row?
We should find the GCF of 65 and 100 GCF of 65 and 100 The common factor is 5. There will be 13 rows of rose plants and 20 rows of sunflower plants.
Explanation
As the GCF of 65 and 100 is 5, the gardener can make rows with 5 plants each.
Now divide 65 and 100 by 5.
There will be 13 rose plants per row and 20 sunflower plants per row.
Problem 2
A teacher has 65 notebooks and 100 pens. She wants to distribute them equally among students with the largest possible equal number of items per student. How many items will each student receive?
GCF of 65 and 100 The common factor is 5. Each student will receive 5 items.
Explanation
There are 65 notebooks and 100 pens.
To find the total number of items each student will receive, we should find the GCF of 65 and 100, which is 5.
Each student will receive 5 items.
Problem 3
A chef has 65 apples and 100 oranges. He wants to pack them into boxes with the longest possible equal number of fruits in each box. How many fruits should be in each box?
For calculating the longest equal number of fruits, we have to calculate the GCF of 65 and 100 The GCF of 65 and 100 The common factor is 5. Each box will have 5 fruits.
Explanation
For calculating the longest number of fruits in each box, we need to calculate the GCF of 65 and 100, which is 5.
Each box will have 5 fruits.
Problem 4
A carpenter has two wooden planks, one 65 cm long and the other 100 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 65 and 100 The common factor is 5. The longest length of each piece is 5 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 65 cm and 100 cm, respectively, we have to find the GCF of 65 and 100, which is 5 cm.
The longest length of each piece is 5 cm.
Problem 5
If the GCF of 65 and ‘a’ is 5, and the LCM is 1300, find ‘a’.
The value of ‘a’ is 100.
Explanation
GCF × LCM = product of the numbers
5 × 1300 = 65 × a
6500 = 65a
a = 6500 ÷ 65 = 100
FAQs on the Greatest Common Factor of 65 and 100
1.What is the LCM of 65 and 100?
2.Is 65 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 100?
5.Are 65 and 100 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 65 and 100?
7.What are some fun ways kids in India can practice GCF of 65 and 100 with numbers?
8.What role do numbers and GCF of 65 and 100 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 65 and 100 skills?
Important Glossaries for GCF of 65 and 100
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 65 are 1, 5, 13, and 65.
- Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 100 is 2² × 5².
- Common Factors: These are factors that are common to two or more numbers. For example, the common factors of 65 and 100 are 1 and 5.
- Greatest Common Factor (GCF): The largest factor that commonly divides two or more numbers. For example, the GCF of 65 and 100 is 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 100 is divided by 65, the remainder is 35.
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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.
