GCF of 15 and 20
2026-02-28 10:27 Diff
https://brightchamps.com/en-us/math/numbers/gcf-of-15-and-20

172 Learners

Last updated on August 12, 2025

The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items and schedule events. In this topic, we will learn about the GCF of 15 and 20.

What is the GCF of 15 and 20?

The greatest common factor of 15 and 20 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.

How to find the GCF of 15 and 20?

To find the GCF of 15 and 20, a few methods are described below -

  1. Listing Factors
  2. Prime Factorization
  3. Long Division Method / by Euclidean Algorithm

GCF of 15 and 20 by Using Listing of factors

Steps to find the GCF of 15 and 20 using the listing of factors

Step 1: Firstly, list the factors of each number Factors of 15 = 1, 3, 5, 15. Factors of 20 = 1, 2, 4, 5, 10, 20.

Step 2: Now, identify the common factors of them Common factors of 15 and 20: 1, 5.

Step 3: Choose the largest factor The largest factor that both numbers have is 5. The GCF of 15 and 20 is 5.

Explore Our Programs

GCF of 15 and 20 Using Prime Factorization

To find the GCF of 15 and 20 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime Factors of 15: 15 = 3 x 5

Prime Factors of 20: 20 = 2 x 2 x 5

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 15 and 20 is 5.

GCF of 15 and 20 Using Division Method or Euclidean Algorithm Method

Find the GCF of 15 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 15 20 ÷ 15 = 1 (quotient), The remainder is calculated as 20 − (15×1) = 5

The remainder is 5, not zero, so continue the process

Step 2: Now divide the previous divisor (15) by the previous remainder (5) Divide 15 by 5 15 ÷ 5 = 3 (quotient), remainder = 15 − (5×3) = 0

The remainder is zero, the divisor will become the GCF. The GCF of 15 and 20 is 5.

Common Mistakes and How to Avoid Them in GCF of 15 and 20

Finding GCF of 15 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 baker has 15 chocolate cupcakes and 20 vanilla cupcakes. She wants to package them into the largest possible number of identical sets. How many cupcakes will be in each set?

Okay, lets begin

We should find the GCF of 15 and 20 GCF of 15 and 20 is 5.

There are 5 equal sets 15 ÷ 5 = 3 20 ÷ 5 = 4

There will be 5 sets, and each set gets 3 chocolate cupcakes and 4 vanilla cupcakes.

Explanation

As the GCF of 15 and 20 is 5, the baker can make 5 sets. Now divide 15 and 20 by 5. Each set gets 3 chocolate cupcakes and 4 vanilla cupcakes.

Well explained 👍

Problem 2

A gardener has 15 roses and 20 tulips. He wants to plant them in rows with the same number of flowers in each row, using the largest possible number of flowers per row. How many flowers will be in each row?

Okay, lets begin

GCF of 15 and 20 is 5. So each row will have 5 flowers.

Explanation

There are 15 roses and 20 tulips. To find the total number of flowers in each row, we should find the GCF of 15 and 20. There will be 5 flowers in each row.

Well explained 👍

Problem 3

A tailor has 15 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 15 and 20 The GCF of 15 and 20 is 5. The length of each piece is 5 meters.

Explanation

To calculate the longest length of the fabric, first, we need to calculate the GCF of 15 and 20, which is 5. The length of each piece of fabric will be 5 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 15 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 15 and 20 is 5. The longest length of each piece is 5 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 15 cm and 20 cm, respectively, we have to find the GCF of 15 and 20, which is 5 cm. The longest length of each piece is 5 cm.

Well explained 👍

Problem 5

If the GCF of 15 and ‘a’ is 5, and the LCM is 60. Find ‘a’.

Okay, lets begin

The value of ‘a’ is 20.

Explanation

GCF x LCM = product of the numbers

5 × 60 = 15 × a

300 = 15a a = 300 ÷ 15 = 20

Well explained 👍

FAQs on the Greatest Common Factor of 15 and 20

1.What is the LCM of 15 and 20?

The LCM of 15 and 20 is 60.

2.Is 15 divisible by 3?

Yes, 15 is divisible by 3 because the sum of its digits (1+5=6) is divisible by 3.

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 2 x 2 x 5.

5.Are 15 and 20 prime numbers?

No, 15 and 20 are not prime numbers because both of them have more than two factors.

Important Glossaries for GCF of 15 and 20

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
  • Prime Factors: These are the 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 the LCM. For example, the LCM of 15 and 20 is 60.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.