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102 LearnersLast updated on September 12, 2025
GCF of 75 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 75 and 100.
What is the GCF of 75 and 100?
The greatest common factor of 75 and 100 is 25. 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 75 and 100?
To find the GCF of 75 and 100, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 75 and 100 by Using Listing of Factors
Steps to find the GCF of 75 and 100 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 75 = 1, 3, 5, 15, 25, 75.
Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100.
Step 2: Now, identify the common factors of them Common factors of 75 and 100: 1, 5, 25.
Step 3: Choose the largest factor The largest factor that both numbers have is 25. The GCF of 75 and 100 is 25.
GCF of 75 and 100 Using Prime Factorization
To find the GCF of 75 and 100 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 5²
Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 2² x 5²
Step 2: Now, identify the common prime factors The common prime factors are: 5 x 5 = 5²
Step 3: Multiply the common prime factors 5² = 25. The Greatest Common Factor of 75 and 100 is 25.
GCF of 75 and 100 Using Division Method or Euclidean Algorithm Method
Find the GCF of 75 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 75 100 ÷ 75 = 1 (quotient), The remainder is calculated as 100 − (75×1) = 25 The remainder is 25, not zero, so continue the process
Step 2: Now divide the previous divisor (75) by the previous remainder (25) Divide 75 by 25 75 ÷ 25 = 3 (quotient), remainder = 75 − (25×3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 75 and 100 is 25.
Common Mistakes and How to Avoid Them in GCF of 75 and 100
Finding GCF of 75 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 75, 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 the 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 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 75 and 100 Examples
Problem 1
A florist has 75 roses and 100 tulips. She wants to create floral arrangements with the largest number of flowers in each without mixing types. How many flowers will be in each arrangement?
We should find the GCF of 75 and 100 GCF of 75 and 100 5² = 25.
There are 25 flowers in each arrangement. 75 ÷ 25 = 3 100 ÷ 25 = 4
There will be 3 arrangements with roses and 4 arrangements with tulips, each containing 25 flowers.
Explanation
As the GCF of 75 and 100 is 25, the florist can make 25-flower arrangements. Now divide 75 and 100 by 25. Each arrangement has 3 sets of roses and 4 sets of tulips.
Problem 2
A coach has 75 red jerseys and 100 blue jerseys. They want to distribute them in sets with an equal number of jerseys, using the largest possible number of jerseys per set. How many jerseys will be in each set?
GCF of 75 and 100 5² = 25.
So each set will have 25 jerseys.
Explanation
There are 75 red and 100 blue jerseys. To find the total number of jerseys in each set, we should find the GCF of 75 and 100. There will be 25 jerseys in each set.
Problem 3
A tailor has 75 meters of red fabric and 100 meters of blue fabric. She wants to cut both fabrics 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 75 and 100 The GCF of 75 and 100
5² = 25.
The fabric is 25 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 75 and 100 which is 25. The length of each piece of the fabric will be 25 meters.
Problem 4
A carpenter has two wooden planks, one 75 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 75 and 100: 5² = 25.
The longest length of each piece is 25 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 75 cm and 100 cm, respectively. We have to find the GCF of 75 and 100, which is 25 cm. The longest length of each piece is 25 cm.
Problem 5
If the GCF of 75 and ‘a’ is 25, and the LCM is 300. Find ‘a’.
The value of ‘a’ is 100.
Explanation
GCF x LCM = product of the numbers
25 × 300 = 75 × a
7500 = 75a
a = 7500 ÷ 75 = 100
FAQs on the Greatest Common Factor of 75 and 100
1.What is the LCM of 75 and 100?
2.Is 75 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 100?
5.Are 75 and 100 prime numbers?
Important Glossaries for GCF of 75 and 100
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 25 are 1, 5, and 25.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 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 75 are 3 and 5.
- 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 75 and 100 is 300.
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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.
