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103 LearnersLast updated on September 9, 2025
GCF of 63 and 54
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 54.
What is the GCF of 63 and 54?
The greatest common factor of 63 and 54 is 9. 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 63 and 54?
To find the GCF of 63 and 54, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 63 and 54 by Using Listing of factors
Steps to find the GCF of 63 and 54 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 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: Now, identify the common factors of them Common factors of 63 and 54: 1, 3, 9.
Step 3: Choose the largest factor The largest factor that both numbers have is 9. The GCF of 63 and 54 is 9.
GCF of 63 and 54 Using Prime Factorization
To find the GCF of 63 and 54 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 54: 54 = 2 x 3 x 3 x 3 = 2 x 3³
Step 2: Now, identify the common prime factors The common prime factors are: 3 x 3 = 3²
Step 3: Multiply the common prime factors 3² = 9. The Greatest Common Factor of 63 and 54 is 9.
GCF of 63 and 54 Using Division Method or Euclidean Algorithm Method
Find the GCF of 63 and 54 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 54 63 ÷ 54 = 1 (quotient), The remainder is calculated as 63 − (54×1) = 9 The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (54) by the previous remainder (9) Divide 54 by 9 54 ÷ 9 = 6 (quotient), remainder = 54 − (9×6) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 63 and 54 is 9.
Common Mistakes and How to Avoid Them in GCF of 63 and 54
Finding the GCF of 63 and 54 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 that 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 54 Examples
Problem 1
An artist has 63 paintbrushes and 54 canvases. She wants to create sets with the largest possible number of items in each set. How many items will be in each set?
We should find the GCF of 63 and 54 GCF of 63 and 54 3² = 9. There are 9 equal sets 63 ÷ 9 = 7 54 ÷ 9 = 6 There will be 9 sets, and each set gets 7 paintbrushes and 6 canvases.
Explanation
As the GCF of 63 and 54 is 9, the artist can make 9 sets.
Now divide 63 and 54 by 9.
Each set gets 7 paintbrushes and 6 canvases.
Problem 2
A gardener has 63 red tulip bulbs and 54 yellow tulip bulbs. She wants to plant them in rows with the same number of bulbs in each row, using the largest possible number of bulbs per row. How many bulbs will be in each row?
GCF of 63 and 54 3² = 9. So each row will have 9 bulbs.
Explanation
There are 63 red and 54 yellow tulip bulbs.
To find the total number of bulbs in each row, we should find the GCF of 63 and 54.
There will be 9 bulbs in each row.
Problem 3
A chef has 63 kilograms of apples and 54 kilograms of oranges. She wants to divide both fruits into portions of equal weight, using the heaviest possible weight. What should be the weight of each portion?
For calculating the heaviest equal weight, we have to calculate the GCF of 63 and 54 The GCF of 63 and 54 3² = 9. The portion is 9 kilograms.
Explanation
For calculating the heaviest weight of the fruits, first, we need to calculate the GCF of 63 and 54, which is 9.
The weight of each portion will be 9 kilograms.
Problem 4
A carpenter has two wooden boards, one 63 cm long and the other 54 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 54 3² = 9. The longest length of each piece is 9 cm.
Explanation
To find the longest length of each piece of the two wooden boards, 63 cm and 54 cm, respectively.
We have to find the GCF of 63 and 54, which is 9 cm.
The longest length of each piece is 9 cm.
Problem 5
If the GCF of 63 and ‘b’ is 9, and the LCM is 378. Find ‘b’.
The value of ‘b’ is 54.
Explanation
GCF x LCM = product of the numbers
9 × 378
= 63 × b 3402
= 63b b
= 3402 ÷ 63 = 54
FAQs on the Greatest Common Factor of 63 and 54
1.What is the LCM of 63 and 54?
2.Is 63 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 54?
5.Are 63 and 54 prime numbers?
Important Glossaries for GCF of 63 and 54
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- 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 21 are 3 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 63 and 54 is 378.
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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.
