103 LearnersLast updated on August 12th, 2025
GCF of 21 and 63
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 21 and 63.
What is the GCF of 21 and 63?
The greatest common factor of 21 and 63 is 21. 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 21 and 63?
To find the GCF of 21 and 63, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 21 and 63 by Using Listing of Factors
Steps to find the GCF of 21 and 63 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 21 = 1, 3, 7, 21. Factors of 63 = 1, 3, 7, 9, 21, 63.
Step 2: Now, identify the common factors of them Common factors of 21 and 63: 1, 3, 7, 21.
Step 3: Choose the largest factor The largest factor that both numbers have is 21. The GCF of 21 and 63 is 21.
GCF of 21 and 63 Using Prime Factorization
To find the GCF of 21 and 63 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 21: 21 = 3 x 7
Prime Factors of 63: 63 = 3 x 3 x 7 = 3² x 7
Step 2: Now, identify the common prime factors The common prime factors are: 3 x 7
Step 3: Multiply the common prime factors 3 x 7 = 21.
The Greatest Common Factor of 21 and 63 is 21.
GCF of 21 and 63 Using Division Method or Euclidean Algorithm Method
Find the GCF of 21 and 63 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 63 by 21 63 ÷ 21 = 3 (quotient), The remainder is calculated as 63 − (21 x 3) = 0
Since the remainder is zero, the divisor will become the GCF. The GCF of 21 and 63 is 21.
Common Mistakes and How to Avoid Them in GCF of 21 and 63
Finding GCF of 21 and 63 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 21, students may mention 5 which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that GCF of two numbers will always be an even number. But it's not true, as a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 21 and 63 Examples
Problem 1
A teacher has 21 apples and 63 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?
We should find GCF of 21 and 63 GCF of 21 and 63 3 x 7 = 21.
There are 21 equal groups 21 ÷ 21 = 1 63 ÷ 21 = 3
There will be 21 groups, and each group gets 1 apple and 3 oranges.
Explanation
As the GCF of 21 and 63 is 21, the teacher can make 21 groups. Now divide 21 and 63 by 21. Each group gets 1 apple and 3 oranges.
Problem 2
A school has 21 red chairs and 63 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 21 and 63 3 x 7 = 21. So each row will have 21 chairs.
Explanation
There are 21 red and 63 blue chairs. To find the total number of chairs in each row, we should find the GCF of 21 and 63. There will be 21 chairs in each row.
Problem 3
A tailor has 21 meters of red ribbon and 63 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 21 and 63 The GCF of 21 and 63 3 x 7 = 21. The ribbon is 21 meters long.
Explanation
For calculating the longest length of the ribbon, first we need to calculate the GCF of 21 and 63 which is 21. The length of each piece of the ribbon will be 21 meters.
Problem 4
A carpenter has two wooden planks, one 21 cm long and the other 63 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 21 and 63 3 x 7 = 21. The longest length of each piece is 21 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 21 cm and 63 cm, respectively. We have to find the GCF of 21 and 63, which is 21 cm. The longest length of each piece is 21 cm.
Problem 5
If the GCF of 21 and ‘a’ is 21, and the LCM is 105. Find ‘a’.
The value of ‘a’ is 63.
Explanation
GCF x LCM = product of the numbers
21 x 105 = 21 x a
2205 = 21a
a = 2205 ÷ 21 = 63
FAQs on the Greatest Common Factor of 21 and 63
1.What is the LCM of 21 and 63?
2.Is 21 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 63?
5.Are 21 and 63 prime numbers?
6.How can children in United Arab Emirates use numbers in everyday life to understand GCF of 21 and 63?
7.What are some fun ways kids in United Arab Emirates can practice GCF of 21 and 63 with numbers?
8.What role do numbers and GCF of 21 and 63 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve GCF of 21 and 63 skills?
Important Glossaries for GCF of 21 and 63
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 21 are 1, 3, 7, and 21.
- 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 21 are 3 and 7.
- Euclidean Algorithm: A method for finding the greatest common factor of two numbers, which involves successive division.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 21 and 63 is 63.
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.
