Last updated on August 2nd, 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 20 and 60.
The greatest common factor of 20 and 60 is 20. 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.
To find the GCF of 20 and 60, a few methods are described below -
Steps to find the GCF of 20 and 60 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 20 = 1, 2, 4, 5, 10, 20.
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Step 2: Now, identify the common factors of them.
Common factors of 20 and 60: 1, 2, 4, 5, 10, 20.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 20.
The GCF of 20 and 60 is 20.
To find the GCF of 20 and 60 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 20: 20 = 2 x 2 x 5 = 2² x 5
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5
Step 2: Now, identify the common prime factors.
The common prime factors are: 2² x 5
Step 3: Multiply the common prime factors.
2² x 5 = 4 x 5 = 20.
The Greatest Common Factor of 20 and 60 is 20.
Find the GCF of 20 and 60 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 60 by 20. 60 ÷ 20 = 3 (quotient),
The remainder is calculated as 60 − (20×3) = 0.
The remainder is zero, so the divisor will become the GCF.
The GCF of 20 and 60 is 20.
Finding the GCF of 20 and 60 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
A teacher has 20 notebooks and 60 markers. 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 20 and 60. GCF of 20 and 60
2² x 5 = 4 x 5 = 20.
There are 20 equal groups. 20 ÷ 20 = 1 60 ÷ 20 = 3
There will be 20 groups, and each group gets 1 notebook and 3 markers.
As the GCF of 20 and 60 is 20, the teacher can make 20 groups.
Now divide 20 and 60 by 20.
Each group gets 1 notebook and 3 markers.
A school has 20 red balls and 60 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 20 and 60 2² x 5 = 4 x 5 = 20.
So each row will have 20 balls.
There are 20 red and 60 blue balls.
To find the total number of balls in each row, we should find the GCF of 20 and 60.
There will be 20 balls in each row.
A tailor has 20 meters of red fabric and 60 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 20 and 60.
The GCF of 20 and 60
2² x 5 = 4 x 5 = 20.
The fabric is 20 meters long.
For calculating the longest length of the fabric, first, we need to calculate the GCF of 20 and 60, which is 20.
The length of each piece of fabric will be 20 meters.
A carpenter has two wooden planks, one 20 cm long and the other 60 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 20 and 60
2² x 5 = 4 x 5 = 20.
The longest length of each piece is 20 cm.
To find the longest length of each piece of the two wooden planks, 20 cm and 60 cm, respectively, we have to find the GCF of 20 and 60, which is 20 cm.
The longest length of each piece is 20 cm.
If the GCF of 20 and ‘a’ is 20, and the LCM is 60, find ‘a’.
The value of ‘a’ is 60.
GCF x LCM = product of the numbers 20 × 60 = 20 × a
1200 = 20a
a = 1200 ÷ 20 = 60
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.