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104 LearnersLast updated on September 20, 2025
GCF of 9 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 9 and 63.
What is the GCF of 9 and 63?
The greatest common factor of 9 and 63 is 9. 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 9 and 63?
To find the GCF of 9 and 63, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 9 and 63 by Using Listing of Factors
Steps to find the GCF of 9 and 63 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 9 = 1, 3, 9.
Factors of 63 = 1, 3, 7, 9, 21, 63.
Step 2: Now, identify the common factors of them: Common factors of 9 and 63: 1, 3, 9.
Step 3: Choose the largest factor: The largest factor that both numbers have is 9.
The GCF of 9 and 63 is 9.
GCF of 9 and 63 Using Prime Factorization
To find the GCF of 9 and 63 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number:
Prime Factors of 9: 9 = 3 x 3 = 3²
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 3 = 3²
Step 3: Multiply the common prime factors: 3² = 9.
The Greatest Common Factor of 9 and 63 is 9.
GCF of 9 and 63 Using Division Method or Euclidean Algorithm Method
Find the GCF of 9 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 9. 63 ÷ 9 = 7 (quotient),
The remainder is calculated as 63 − (9×7) = 0.
The remainder is zero, so the divisor becomes the GCF.
The GCF of 9 and 63 is 9.
Common Mistakes and How to Avoid Them in GCF of 9 and 63
Finding the GCF of 9 and 63 may seem 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 9, students may mention 6, 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 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 9 and 63 Examples
Problem 1
A gardener has 9 rose plants and 63 tulip plants. She wants to plant them in rows with the largest possible equal number of plants in each row. How many plants will be in each row?
We should find the GCF of 9 and 63. GCF of 9 and 63 is 9.
There are 9 equal groups. 9 ÷ 9 = 1 63 ÷ 9 = 7
There will be 9 groups, and each group gets 1 rose plant and 7 tulip plants.
Explanation
As the GCF of 9 and 63 is 9, the gardener can make 9 groups.
Now divide 9 and 63 by 9.
Each group gets 1 rose plant and 7 tulip plants.
Problem 2
A school has 9 basketballs and 63 soccer 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?
GCF of 9 and 63 is 9. So each row will have 9 balls.
Explanation
There are 9 basketballs and 63 soccer balls.
To find the total number of balls in each row, we should find the GCF of 9 and 63.
There will be 9 balls in each row.
Problem 3
A chef has 9 kg of apples and 63 kg of oranges. She wants to pack them into boxes of equal weight, using the largest possible weight. What should be the weight of each box?
For calculating the largest equal weight, we have to calculate the GCF of 9 and 63.
The GCF of 9 and 63 is 9.
The weight of each box is 9 kg.
Explanation
For calculating the largest weight of the boxes first, we need to calculate the GCF of 9 and 63, which is 9.
The weight of each box will be 9 kg.
Problem 4
A carpenter has two wooden planks, one 9 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 9 and 63 is 9.
The longest length of each piece is 9 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 9 cm and 63 cm, respectively.
We have to find the GCF of 9 and 63, which is 9 cm.
The longest length of each piece is 9 cm.
Problem 5
If the GCF of 9 and ‘b’ is 9, and the LCM is 189, find ‘b’.
The value of ‘b’ is 63.
Explanation
GCF x LCM = product of the numbers
9 × 189 = 9 × b
1701 = 9b
b = 1701 ÷ 9 = 189
FAQs on the Greatest Common Factor of 9 and 63
1.What is the LCM of 9 and 63?
2.Is 9 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 63?
5.Are 9 and 63 prime numbers?
Important Glossaries for GCF of 9 and 63
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- 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 63 are 3 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 8 is divided by 3, the remainder is 2 and the quotient is 2.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 9 and 63 is 9, as it is their largest common factor that divides the numbers completely.
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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.
