GCF of 7 and 21
2026-02-28 21:45 Diff
https://brightchamps.com/en-us/math/numbers/gcf-of-7-and-21

198 Learners

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 the items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 7 and 21.

What is the GCF of 7 and 21?

The greatest common factor of 7 and 21 is 7. 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 7 and 21?

To find the GCF of 7 and 21, a few methods are described below:

  • Listing Factors
     
  • Prime Factorization
     
  • Long Division Method or Euclidean Algorithm

GCF of 7 and 21 by Using Listing of factors

Steps to find the GCF of 7 and 21 using the listing of factors:

Step 1: Firstly, list the factors of each number:

Factors of 7 = 1, 7.

Factors of 21 = 1, 3, 7, 21.

Step 2: Now, identify the common factors of them Common factors of 7 and 21: 1, 7.

Step 3: Choose the largest factor The largest factor that both numbers have is 7. The GCF of 7 and 21 is 7.

Explore Our Programs

GCF of 7 and 21 Using Prime Factorization

To find the GCF of 7 and 21 using the Prime Factorization Method, follow these steps:

Step 1: Find the prime factors of each number

Prime factors of 7: 7 = 7

factors of 21: 21 = 3 x 7

Step 2: Now, identify the common prime factors The common prime factor is 7.

Step 3: Multiply the common prime factors The Greatest Common Factor of 7 and 21 is 7.

GCF of 7 and 21 Using Division Method or Euclidean Algorithm Method

Find the GCF of 7 and 21 using the division method or Euclidean Algorithm Method. Follow these steps:

Step 1: First, divide the larger number by the smaller number Here, divide 21 by 7 21 ÷ 7 = 3 (quotient),

The remainder is calculated as 21 − (7×3) = 0

The remainder is zero, so the divisor will become the GCF.

The GCF of 7 and 21 is 7.

Common Mistakes and How to Avoid Them in GCF of 7 and 21

Finding GCF of 7 and 21 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.

Problem 1

A teacher has 7 apples and 21 oranges. 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?

Okay, lets begin

We should find the GCF of 7 and 21 GCF of 7 and 21

There are 7 equal groups

7 ÷ 7 = 1

21 ÷ 7 = 3

There will be 7 groups, and each group gets 1 apple and 3 oranges.

Explanation

As the GCF of 7 and 21 is 7, the teacher can make 7 groups.

Now divide 7 and 21 by 7.

Each group gets 1 apple and 3 oranges.

Well explained 👍

Problem 2

A school has 7 red balls and 21 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?

Okay, lets begin

GCF of 7 and 21 7 So each row will have 7 balls.

Explanation

There are 7 red and 21 blue balls.

To find the total number of balls in each row, we should find the GCF of 7 and 21.

There will be 7 balls in each row.

Well explained 👍

Problem 3

A tailor has 7 meters of red fabric and 21 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 7 and 21 The GCF of 7 and 21 7 The fabric is 7 meters long.

Explanation

For calculating the longest length of the fabric first we need to calculate the GCF of 7 and 21 which is 7. The length of each piece of fabric will be 7 meters.

Well explained 👍

Problem 4

A carpenter has two wooden planks, one 7 cm long and the other 21 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 7 and 21

The longest length of each piece is 7 cm.

Explanation

To find the longest length of each piece of the two wooden planks, 7 cm and 21 cm, respectively, we have to find the GCF of 7 and 21, which is 7 cm. The longest length of each piece is 7 cm.

Well explained 👍

Problem 5

If the GCF of 7 and ‘b’ is 7, and the LCM is 21, find ‘b’.

Okay, lets begin

The value of ‘b’ is 21.

Explanation

GCF x LCM = product of the numbers

7 × 21 = 7 × b

147 = 7b

b = 147 ÷ 7 = 21

Well explained 👍

FAQs on the Greatest Common Factor of 7 and 21

1.What is the LCM of 7 and 21?

The LCM of 7 and 21 is 21.

2.Is 7 divisible by 2?

No, 7 is not divisible by 2 because it is an odd 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 21?

The prime factorization of 21 is 3 x 7.

5.Are 7 and 21 prime numbers?

No, 7 is a prime number because it has only two factors, 1 and 7. However, 21 is not a prime number because it has more than two factors.

Important Glossaries for GCF of 7 and 21

  • Factors: Factors are numbers that divide the target number completely. For example, the factors of 7 are 1 and 7.
  • Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 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 21 are 3 and 7.
  • Remainder: The value left after division when the number cannot be divided evenly. For example, when 21 is divided by 7, the remainder is 0.
  • LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 7 and 21 is 21.

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.