GCF of 100 and 250
2026-02-28 09:11 Diff
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Last updated on September 20, 2025

The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 100 and 250.

What is the GCF of 100 and 250?

The greatest common factor of 100 and 250 is 50. 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 100 and 250?

To find the GCF of 100 and 250, a few methods are described below 

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method / by Euclidean Algorithm

GCF of 100 and 250 by Using Listing of Factors

Steps to find the GCF of 100 and 250 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 250 = 1, 2, 5, 10, 25, 50, 125, 250.

Step 2: Now, identify the common factors Common factors of 100 and 250: 1, 2, 5, 10, 25, 50.

Step 3: Choose the largest factor The largest factor that both numbers have is 50.

The GCF of 100 and 250 is 50.

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GCF of 100 and 250 Using Prime Factorization

To find the GCF of 100 and 250 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 250: 250 = 2 × 5 × 5 × 5 = 2 × 5³

Step 2: Now, identify the common prime factors The common prime factors are: 2 × 5 × 5 = 2 × 5²

Step 3: Multiply the common prime factors 2 × 5² = 2 × 25 = 50.

The Greatest Common Factor of 100 and 250 is 50.

GCF of 100 and 250 Using Division Method or Euclidean Algorithm Method

Find the GCF of 100 and 250 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number

Here, divide 250 by 100 250 ÷ 100 = 2 (quotient),

The remainder is calculated as 250 − (100×2) = 50

The remainder is 50, not zero, so continue the process

Step 2: Now divide the previous divisor (100) by the previous remainder (50)

Divide 100 by 50 100 ÷ 50 = 2 (quotient), remainder = 100 − (50×2) = 0

The remainder is zero, the divisor will become the GCF.

The GCF of 100 and 250 is 50.

Common Mistakes and How to Avoid Them in GCF of 100 and 250

Finding the GCF of 100 and 250 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.

Problem 1

A chef has 100 apples and 250 oranges. He wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?

Okay, lets begin

We should find the GCF of 100 and 250 GCF of 100 and 250

2 × 5² = 2 × 25 = 50.

There are 50 equal groups 100 ÷ 50 = 2 250 ÷ 50 = 5

There will be 50 groups, and each group gets 2 apples and 5 oranges.

Explanation

As the GCF of 100 and 250 is 50, the chef can make 50 groups.

Now divide 100 and 250 by 50.

Each group gets 2 apples and 5 oranges.

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Problem 2

A school has 100 red books and 250 blue books. They want to arrange them in rows with the same number of books in each row, using the largest possible number of books per row. How many books will be in each row?

Okay, lets begin

GCF of 100 and 250 2 × 5² = 2 × 25 = 50. So each row will have 50 books.

Explanation

There are 100 red and 250 blue books.

To find the total number of books in each row, we should find the GCF of 100 and 250.

There will be 50 books in each row.

Well explained 👍

Problem 3

A tailor has 100 meters of red fabric and 250 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?

Okay, lets begin

For calculating the longest equal length, we have to calculate the GCF of 100 and 250

The GCF of 100 and 250 2 × 5² = 2 × 25 = 50.

The fabric is 50 meters long.

Explanation

For calculating the longest length of the fabric, first we need to calculate the GCF of 100 and 250, which is 50.

The length of each piece of the fabric will be 50 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 100 cm long and the other 250 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?

Okay, lets begin

The carpenter needs the longest piece of wood GCF of 100 and 250

2 × 5² = 2 × 25 = 50.

The longest length of each piece is 50 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 100 cm and 250 cm, respectively, we have to find the GCF of 100 and 250, which is 50 cm.

The longest length of each piece is 50 cm.

Well explained 👍

Problem 5

If the GCF of 100 and ‘b’ is 50, and the LCM is 500. Find ‘b’.

Okay, lets begin

The value of ‘b’ is 250.

Explanation

GCF × LCM = product of the numbers

50 × 500 = 100 × b

25000 = 100b

b = 25000 ÷ 100 = 250

Well explained 👍

FAQs on the Greatest Common Factor of 100 and 250

1.What is the LCM of 100 and 250?

The LCM of 100 and 250 is 500.

2.Is 100 divisible by 4?

Yes, 100 is divisible by 4 because 100 ÷ 4 = 25, which is a whole number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 250?

The prime factorization of 250 is 2 × 5³.

5.Are 100 and 250 prime numbers?

No, 100 and 250 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 100 and 250

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 50 are 1, 2, 5, 10, 25, and 50.
  • 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 20 are 2 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 100 and 250 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.