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 100 and 80.
The greatest common factor of 100 and 80 is 20. 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 100 and 80, a few methods are described below -
Steps to find the GCF of 100 and 80 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 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.
Step 2: Now, identify the common factors of them Common factors of 100 and 80: 1, 2, 4, 5, 10, 20.
Step 3: Choose the largest factor
The largest factor that both numbers have is 20.
The GCF of 100 and 80 is 20.
To find the GCF of 100 and 80 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 2² x 5²
Prime Factors of 80: 80 = 2 x 2 x 2 x 2 x 5 = 2⁴ x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 5 = 2² x 5
Step 3: Multiply the common prime factors 2² x 5 = 4 x 5 = 20.
The Greatest Common Factor of 100 and 80 is 20.
Find the GCF of 100 and 80 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 100 by 80 100 ÷ 80 = 1 (quotient),
The remainder is calculated as 100 − (80 x 1) = 20
The remainder is 20, not zero, so continue the process
Step 2: Now divide the previous divisor (80) by the previous remainder (20)
Divide 80 by 20 80 ÷ 20 = 4 (quotient), remainder = 80 − (20 x 4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 100 and 80 is 20.
Finding GCF of 100 and 80 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A teacher has 100 pencils and 80 erasers. She 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 100 and 80 GCF of 100 and 80 2² x 5 = 4 x 5 = 20.
There are 20 equal groups 100 ÷ 20 = 5
80 ÷ 20 = 4
There will be 20 groups, and each group gets 5 pencils and 4 erasers.
As the GCF of 100 and 80 is 20, the teacher can make 20 groups. Now divide 100 and 80 by 20. Each group gets 5 pencils and 4 erasers.
A school has 100 red chairs and 80 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 80 2² x 5 = 4 × 5 = 20.
So each row will have 20 chairs.
There are 100 red and 80 blue chairs. To find the total number of chairs in each row, we should find the GCF of 100 and 80. There will be 20 chairs in each row.
A tailor has 100 meters of red ribbon and 80 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 80
The GCF of 100 and 80 2² x 5 = 4 × 5 = 20.
The ribbon is 20 meters long.
For calculating the longest length of the ribbon first, we need to calculate the GCF of 100 and 80, which is 20. The length of each piece of the ribbon will be 20 meters.
A carpenter has two wooden planks, one 100 cm long and the other 80 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 80
2² x 5 = 4 × 5 = 20.
The longest length of each piece is 20 cm.
To find the longest length of each piece of the two wooden planks, 100 cm and 80 cm, respectively. We have to find the GCF of 100 and 80, which is 20 cm. The longest length of each piece is 20 cm.
If the GCF of 100 and ‘a’ is 20, and the LCM is 400. Find ‘a’.
The value of ‘a’ is 80.
GCF x LCM = product of the numbers 20 × 400 = 100 × a
8000 = 100a
a = 8000 ÷ 100 = 80
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.