GCF of 50 and 75
2026-02-28 23:59 Diff
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Last updated on August 5, 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, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 50 and 75.

What is the GCF of 50 and 75?

The greatest common factor of 50 and 75 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 50 and 75?

To find the GCF of 50 and 75, a few methods are described below:

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

GCF of 50 and 75 by Using Listing of Factors

Steps to find the GCF of 50 and 75 using the listing of factors:

Step 1: Firstly, list the factors of each number:

Factors of 50 = 1, 2, 5, 10, 25, 50.

Factors of 75 = 1, 3, 5, 15, 25, 75.

Step 2: Now, identify the common factors of them Common factors of 50 and 75: 1, 5, 25.

Step 3: Choose the largest factor:

The largest factor that both numbers have is 25.

The GCF of 50 and 75 is 25.

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GCF of 50 and 75 Using Prime Factorization

To find the GCF of 50 and 75 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 50: 50 = 2 x 5 x 5 = 2 x 5²

Prime Factors of 75: 75 = 3 x 5 x 5 = 3 x 5²

Step 2: Now, identify the common prime factors The common prime factor is: 5 x 5 = 5²

Step 3: Multiply the common prime factors 5² = 25. The Greatest Common Factor of 50 and 75 is 25.

GCF of 50 and 75 Using Division Method or Euclidean Algorithm Method

Find the GCF of 50 and 75 using the division method or Euclidean Algorithm Method. Follow these steps:

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

Here, divide 75 by 50 75 ÷ 50 = 1 (quotient), The remainder is calculated as 75 − (50×1) = 25

The remainder is 25, not zero, so continue the process

Step 2: Now divide the previous divisor (50) by the previous remainder (25)

Divide 50 by 25 50 ÷ 25 = 2 (quotient), remainder = 50 − (25×2) = 0

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

The GCF of 50 and 75 is 25.

Common Mistakes and How to Avoid Them in GCF of 50 and 75

Finding GCF of 50 and 75 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 50 apples and 75 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 50 and 75 GCF of 50 and 75

5² = 25.

There are 25 equal groups

50 ÷ 25 = 2

75 ÷ 25 = 3

There will be 25 groups, and each group gets 2 apples and 3 oranges.

Explanation

As the GCF of 50 and 75 is 25, the chef can make 25 groups.

Now divide 50 and 75 by 25.

Each group gets 2 apples and 3 oranges.

Well explained 👍

Problem 2

A school has 50 desks and 75 chairs. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?

Okay, lets begin

GCF of 50 and 75 5² = 25. So each row will have 25 items.

Explanation

There are 50 desks and 75 chairs. To find the total number of items in each row, we should find the GCF of 50 and 75. There will be 25 items in each row.

Well explained 👍

Problem 3

A tailor has 50 meters of red fabric and 75 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 50 and 75.

The GCF of 50 and 75

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 50 and 75, which is 25. The length of each piece of fabric will be 25 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 50 cm long and the other 75 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 50 and 75

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, 50 cm and 75 cm, respectively.

We have to find the GCF of 50 and 75, which is 25 cm.

The longest length of each piece is 25 cm.

Well explained 👍

Problem 5

If the GCF of 50 and ‘b’ is 25, and the LCM is 150, find ‘b’.

Okay, lets begin

The value of ‘b’ is 75.

Explanation

GCF x LCM = product of the numbers

25 × 150 = 50 × b

3750 = 50b

b = 3750 ÷ 50 = 75

Well explained 👍

FAQs on the Greatest Common Factor of 50 and 75

1.What is the LCM of 50 and 75?

The LCM of 50 and 75 is 150.

2.Is 50 divisible by 2?

Yes, 50 is divisible by 2 because it is an even 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 75?

The prime factorization of 75 is 3 x 5².

5.Are 50 and 75 prime numbers?

No, 50 and 75 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 50 and 75

  • 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 11 is divided by 7, the remainder is 4 and the quotient is 1.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 50 and 75 is 150.

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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.