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 8 and 20.
The greatest common factor of 8 and 20 is 4. 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 8 and 20, a few methods are described below
Steps to find the GCF of 8 and 20 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 8 = 1, 2, 4, 8.
Factors of 20 = 1, 2, 4, 5, 10, 20.
Step 2: Now, identify the common factors of them Common factors of 8 and 20: 1, 2, 4.
Step 3: Choose the largest factor
The largest factor that both numbers have is 4.
The GCF of 8 and 20 is 4.
To find the GCF of 8 and 20 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 8: 8 = 2 × 2 × 2 = 2³
Prime Factors of 20: 20 = 2 × 2 × 5 = 2² × 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 × 2 = 2²
Step 3: Multiply the common prime factors 2² = 4.
The Greatest Common Factor of 8 and 20 is 4.
Find the GCF of 8 and 20 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 20 by 8 20 ÷ 8 = 2 (quotient), The remainder is calculated as 20 − (8 × 2) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (8) by the previous remainder (4)
Divide 8 by 4 8 ÷ 4 = 2 (quotient), remainder = 8 − (4 × 2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 8 and 20 is 4.
Finding GCF of 8 and 20 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
A gardener has 8 apple trees and 20 orange trees. She wants to plant them in groups with the same number of trees in each group. What is the largest number of trees that can be planted in each group?
We should find the GCF of 8 and 20. GCF of 8 and 20 2² = 4.
There are 4 equal groups. 8 ÷ 4 = 2 20 ÷ 4 = 5
There will be 4 groups, and each group gets 2 apple trees and 5 orange trees.
As the GCF of 8 and 20 is 4, the gardener can make 4 groups.
Now divide 8 and 20 by 4.
Each group gets 2 apple trees and 5 orange trees.
A school has 8 red balloons and 20 blue balloons. They want to arrange them in rows with the same number of balloons in each row, using the largest possible number of balloons per row. How many balloons will be in each row?
GCF of 8 and 20 2² = 4. So each row will have 4 balloons.
There are 8 red and 20 blue balloons.
To find the total number of balloons in each row, we should find the GCF of 8 and 20.
There will be 4 balloons in each row.
A tailor has 8 meters of red fabric and 20 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 8 and 20.
The GCF of 8 and 20 2² = 4.
The fabric pieces will each be 4 meters long.
For calculating the longest length of the fabric, first we need to calculate the GCF of 8 and 20, which is 4.
The length of each piece of fabric will be 4 meters.
A carpenter has two wooden planks, one 8 cm long and the other 20 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 8 and 20 2² = 4.
The longest length of each piece is 4 cm.
To find the longest length of each piece of the two wooden planks, 8 cm and 20 cm, respectively, we have to find the GCF of 8 and 20, which is 4 cm.
The longest length of each piece is 4 cm.
If the GCF of 8 and ‘a’ is 4, and the LCM is 40, find ‘a’.
The value of ‘a’ is 10.
GCF × LCM = product of the numbers 4 × 40 = 8 × a
160 = 8a
a = 160 ÷ 8 = 20
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.