103 LearnersLast updated on August 12, 2025
GCF of 63 and 84
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 63 and 84.
What is the GCF of 63 and 84?
The greatest common factor of 63 and 84 is 21. 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 63 and 84?
To find the GCF of 63 and 84, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 63 and 84 by Using Listing of Factors
Steps to find the GCF of 63 and 84 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 63 = 1, 3, 7, 9, 21, 63.
Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Step 2: Now, identify the common factors of them Common factors of 63 and 84: 1, 3, 7, 21.
Step 3: Choose the largest factor The largest factor that both numbers have is 21.
The GCF of 63 and 84 is 21.
GCF of 63 and 84 Using Prime Factorization
To find the GCF of 63 and 84 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 63: 63 = 3 x 3 x 7 = 3² x 7
Prime Factors of 84: 84 = 2 x 2 x 3 x 7 = 2² x 3 x 7
Step 2: Now, identify the common prime factors The common prime factors are: 3 x 7 = 21
Step 3: Multiply the common prime factors 3 x 7 = 21. The Greatest Common Factor of 63 and 84 is 21.
GCF of 63 and 84 Using Division Method or Euclidean Algorithm Method
Find the GCF of 63 and 84 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 84 by 63 84 ÷ 63 = 1 (quotient), The remainder is calculated as 84 - (63 x 1) = 21 The remainder is 21, not zero, so continue the process
Step 2: Now divide the previous divisor (63) by the previous remainder (21) Divide 63 by 21 63 ÷ 21 = 3 (quotient), remainder = 63 - (21 x 3) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 63 and 84 is 21.
Common Mistakes and How to Avoid Them in GCF of 63 and 84
Finding the GCF of 63 and 84 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 63, 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 the GCF of two numbers will always be an even number. But it's not true; 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 63 and 84 Examples
Problem 1
A gardener has 63 tulip bulbs and 84 daffodil bulbs. She wants to plant them in rows with the same number of bulbs in each row, using the largest possible number. How many bulbs will be in each row?
We should find the GCF of 63 and 84 GCF of 63 and 84 3 x 7 = 21. There are 21 equal groups 63 ÷ 21 = 3 84 ÷ 21 = 4 There will be 21 groups, and each group gets 3 tulip bulbs and 4 daffodil bulbs.
Explanation
As the GCF of 63 and 84 is 21, the gardener can make 21 groups. Now divide 63 and 84 by 21. Each group gets 3 tulip bulbs and 4 daffodil bulbs.
Problem 2
A chef has 63 apples and 84 bananas. He wants to make fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
GCF of 63 and 84 3 x 7 = 21. So each basket will have 21 fruits.
Explanation
There are 63 apples and 84 bananas. To find the total number of fruits in each basket, we should find the GCF of 63 and 84. There will be 21 fruits in each basket.
Problem 3
A tailor has 63 meters of cotton fabric and 84 meters of silk 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 63 and 84 The GCF of 63 and 84 3 x 7 = 21. The fabric is 21 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 63 and 84, which is 21. The length of each piece of fabric will be 21 meters.
Problem 4
A carpenter has two wooden planks, one 63 cm long and the other 84 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 63 and 84 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, 63 cm and 84 cm, respectively, we have to find the GCF of 63 and 84, which is 21 cm. The longest length of each piece is 21 cm.
Problem 5
If the GCF of 63 and ‘b’ is 21, and the LCM is 252. Find ‘b’.
The value of ‘b’ is 84.
Explanation
GCF x LCM = product of the numbers
21 x 252 = 63 x b
5292 = 63b
b = 5292 ÷ 63 = 84
FAQs on the Greatest Common Factor of 63 and 84
1.What is the LCM of 63 and 84?
2.Is 63 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 84?
5.Are 63 and 84 prime numbers?
6.How can children in Canada use numbers in everyday life to understand GCF of 63 and 84?
7.What are some fun ways kids in Canada can practice GCF of 63 and 84 with numbers?
8.What role do numbers and GCF of 63 and 84 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve GCF of 63 and 84 skills?
Important Glossaries for GCF of 63 and 84
- 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 7 are 7, 14, 21, 28, 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 84 are 2, 3, and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 84 is divided by 63, the remainder is 21 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 63 and 84 is 252.
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.
