GCF of 8 and 20
2026-02-28 10:48 Diff
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Last updated on August 5, 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.

What is 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.

How to find the GCF of 8 and 20?

To find the GCF of 8 and 20, a few methods are described below

  • Listing Factors
  • Prime Factorization
  • Long Division Method / by Euclidean Algorithm

GCF of 8 and 20 by Using Listing of Factors

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.

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GCF of 8 and 20 Using Prime Factorization

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.

GCF of 8 and 20 Using Division Method or Euclidean Algorithm Method

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.

Common Mistakes and How to Avoid Them in GCF of 8 and 20

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.

Problem 1

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?

Okay, lets begin

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.

Explanation

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.

Well explained 👍

Problem 2

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?

Okay, lets begin

GCF of 8 and 20 2² = 4. So each row will have 4 balloons.

Explanation

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.

Well explained 👍

Problem 3

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?

Okay, lets begin

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.

Explanation

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.

Well explained 👍

Problem 4

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?

Okay, lets begin

The carpenter needs the longest piece of wood.

GCF of 8 and 20 2² = 4.

The longest length of each piece is 4 cm.

Explanation

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.

Well explained 👍

Problem 5

If the GCF of 8 and ‘a’ is 4, and the LCM is 40, find ‘a’.

Okay, lets begin

The value of ‘a’ is 10.

Explanation

GCF × LCM = product of the numbers 4 × 40 = 8 × a

160 = 8a

a = 160 ÷ 8 = 20

Well explained 👍

FAQs on the Greatest Common Factor of 8 and 20

1.What is the LCM of 8 and 20?

The LCM of 8 and 20 is 40.

2.Is 8 divisible by 2?

Yes, 8 is divisible by 2 because it is an even number.

3.What will be the GCF of any two prime numbers?

The common factor of prime numbers is 1 and the number itself. Since 1 is the only common factor of any two prime numbers, it is said to be the GCF of any two prime numbers.

4.What is the prime factorization of 20?

The prime factorization of 20 is 2² × 5.

5.Are 8 and 20 prime numbers?

No, 8 and 20 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 8 and 20

  • Factors: Numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
  • Multiple: Products obtained by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, and so on.
  • Prime Factors: Factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 20 are 2 and 5.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 20 is divided by 6, the remainder is 2 and the quotient is 3.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 20 is 40.

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Hiralee Lalitkumar Makwana

About the Author

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.

Fun Fact

: She loves to read number jokes and games.