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106 LearnersLast updated on September 23, 2025
GCF of 100 and 125
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 100 and 125.
What is the GCF of 100 and 125?
The greatest common factor of 100 and 125 is 25. 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 100 and 125?
To find the GCF of 100 and 125, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 100 and 125 by Using Listing of Factors
Steps to find the GCF of 100 and 125 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100. Factors of 125 = 1, 5, 25, 125.
Step 2: Now, identify the common factors of them Common factors of 100 and 125: 1, 5, 25.
Step 3: Choose the largest factor The largest factor that both numbers have is 25. The GCF of 100 and 125 is 25.
GCF of 100 and 125 Using Prime Factorization
To find the GCF of 100 and 125 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 100: 100 = 2 × 2 × 5 × 5 = 2² × 5²
Prime Factors of 125: 125 = 5 × 5 × 5 = 5³
Step 2: Now, identify the common prime factors The common prime factors are: 5 × 5 = 5²
Step 3: Multiply the common prime factors 5² = 25.
The Greatest Common Factor of 100 and 125 is 25.
GCF of 100 and 125 Using Division Method or Euclidean Algorithm Method
Find the GCF of 100 and 125 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 125 by 100 125 ÷ 100 = 1 (quotient), The remainder is calculated as 125 − (100×1) = 25 The remainder is 25, not zero, so continue the process
Step 2: Now divide the previous divisor (100) by the previous remainder (25) Divide 100 by 25 100 ÷ 25 = 4 (quotient), remainder = 100 − (25×4) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 100 and 125 is 25.
Common Mistakes and How to Avoid Them in GCF of 100 and 125
Finding GCF of 100 and 125 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 100, students may mention 30, 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 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 100 and 125 Examples
Problem 1
A gardener has 100 tulip bulbs and 125 daffodil bulbs. She wants to plant them in equal groups with the largest number of bulbs in each group. How many bulbs will be in each group?
We should find the GCF of 100 and 125 GCF of 100 and 125 5² = 25.
There are 25 equal groups 100 ÷ 25 = 4 125 ÷ 25 = 5
There will be 25 groups, and each group gets 4 tulip bulbs and 5 daffodil bulbs.
Explanation
As the GCF of 100 and 125 is 25, the gardener can make 25 groups.
Now divide 100 and 125 by 25. Each group gets 4 tulip bulbs and 5 daffodil bulbs.
Problem 2
A school has 100 red chairs and 125 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 100 and 125 5² = 25.
So each row will have 25 chairs.
Explanation
There are 100 red and 125 blue chairs. To find the total number of chairs in each row, we should find the GCF of 100 and 125. There will be 25 chairs in each row.
Problem 3
A tailor has 100 meters of red ribbon and 125 meters of blue ribbon. She wants to cut both ribbons 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 100 and 125
The GCF of 100 and 125 5² = 25.
The ribbon is 25 meters long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 100 and 125, which is 25.
The length of each piece of the ribbon will be 25 meters.
Problem 4
A carpenter has two wooden planks, one 100 cm long and the other 125 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 100 and 125 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, 100 cm and 125 cm, respectively.
We have to find the GCF of 100 and 125, which is 25 cm. The longest length of each piece is 25 cm.
Problem 5
If the GCF of 100 and ‘b’ is 25, and the LCM is 500. Find ‘b’.
The value of ‘b’ is 125.
Explanation
GCF x LCM = product of the numbers
25 × 500 = 100 × b
12500 = 100b
b = 12500 ÷ 100 = 125
FAQs on the Greatest Common Factor of 100 and 125
1.What is the LCM of 100 and 125?
2.Is 100 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 125?
5.Are 100 and 125 prime numbers?
Important Glossaries for GCF of 100 and 125
- 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 50 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 100 and 125 is 500.
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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.
