Last updated on August 5th, 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.
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.
To find the GCF of 50 and 75, a few methods are described below:
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.
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.
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.
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.
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?
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.
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.
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?
GCF of 50 and 75 5² = 25. So each row will have 25 items.
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.
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?
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.
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.
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?
The carpenter needs the longest piece of wood GCF of 50 and 75
5² = 25.
The longest length of each piece is 25 cm.
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.
If the GCF of 50 and ‘b’ is 25, and the LCM is 150, find ‘b’.
The value of ‘b’ is 75.
GCF x LCM = product of the numbers
25 × 150 = 50 × b
3750 = 50b
b = 3750 ÷ 50 = 75
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.
: She loves to read number jokes and games.