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 80 and 125.
The greatest common factor of 80 and 125 is 5. 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 80 and 125, a few methods are described below -
Steps to find the GCF of 80 and 125 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Factors of 125 = 1, 5, 25, 125.
Step 2: Now, identify the common factors of them Common factors of 80 and 125: 1, 5.
Step 3: Choose the largest factor
The largest factor that both numbers have is 5.
The GCF of 80 and 125 is 5.
To find the GCF of 80 and 125 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 80: 80 = 2 x 2 x 2 x 2 x 5 = 2^4 x 5
Prime Factors of 125: 125 = 5 x 5 x 5 = 5^3
Step 2: Now, identify the common prime factors
The common prime factor is: 5
Step 3: Multiply the common prime factors 5 = 5.
The Greatest Common Factor of 80 and 125 is 5.
Find the GCF of 80 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 80 125 ÷ 80 = 1 (quotient),
The remainder is calculated as 125 − (80 x 1) = 45
The remainder is 45, not zero, so continue the process
Step 2: Now divide the previous divisor (80) by the previous remainder (45)
Divide 80 by 45 80 ÷ 45 = 1 (quotient), remainder = 80 − (45 x 1) = 35
Continue the process
Step 3: Now divide the previous divisor (45) by the previous remainder (35)
Divide 45 by 35 45 ÷ 35 = 1 (quotient), remainder = 45 − (35 x 1) = 10
Continue the process
Step 4: Now divide the previous divisor (35) by the previous remainder (10)
Divide 35 by 10 35 ÷ 10 = 3 (quotient), remainder = 35 − (10 x 3) = 5
Continue the process
Step 5: Now divide the previous divisor (10) by the previous remainder (5)
Divide 10 by 5 10 ÷ 5 = 2 (quotient), remainder = 10 − (5 x 2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 80 and 125 is 5.
Finding the GCF of 80 and 125 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 80 apples and 125 bananas. She wants to create fruit baskets with the largest number of items in each basket. How many items will be in each basket?
We should find the GCF of 80 and 125 GCF of 80 and 125 = 5.
There are 5 equal groups 80 ÷ 5 = 16
125 ÷ 5 = 25
There will be 5 baskets, and each basket gets 16 apples and 25 bananas.
As the GCF of 80 and 125 is 5, the chef can make 5 baskets. Now divide 80 and 125 by 5. Each basket gets 16 apples and 25 bananas.
A school has 80 red balls and 125 blue balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?
GCF of 80 and 125 = 5.
So each row will have 5 balls.
There are 80 red and 125 blue balls. To find the total number of balls in each row, we should find the GCF of 80 and 125. There will be 5 balls in each row.
A tailor has 80 meters of red fabric and 125 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 80 and 125
The GCF of 80 and 125 = 5
Each piece of fabric will be 5 meters long.
For calculating the longest length of the fabric first we need to calculate the GCF of 80 and 125, which is 5. The length of each piece of the fabric will be 5 meters.
A carpenter has two wooden planks, one 80 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 80 and 125 = 5.
The longest length of each piece is 5 cm.
To find the longest length of each piece of the two wooden planks, 80 cm and 125 cm, respectively. We have to find the GCF of 80 and 125, which is 5 cm. The longest length of each piece is 5 cm.
If the GCF of 80 and ‘b’ is 5, and the LCM is 2000. Find ‘b’.
The value of ‘b’ is 125.
GCF x LCM = product of the numbers 5 × 2000 = 80 × b
10000 = 80b
b = 10000 ÷ 80 = 125
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.