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103 LearnersLast updated on September 9, 2025
GCF of 9 and 45
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 9 and 45.
What is the GCF of 9 and 45?
The greatest common factor of 9 and 45 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 45?
To find the GCF of 9 and 45, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 9 and 45 by Using Listing of Factors
Steps to find the GCF of 9 and 45 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 9 = 1, 3, 9. Factors of 45 = 1, 3, 5, 9, 15, 45.
Step 2: Now, identify the common factors of them Common factors of 9 and 45: 1, 3, 9.
Step 3: Choose the largest factor The largest factor that both numbers have is 9. The GCF of 9 and 45 is 9.
GCF of 9 and 45 Using Prime Factorization
To find the GCF of 9 and 45 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 45: 45 = 3 x 3 x 5 = 3² x 5
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 45 is 9.
GCF of 9 and 45 Using Division Method or Euclidean Algorithm Method
Find the GCF of 9 and 45 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 45 by 9 45 ÷ 9 = 5 (quotient), The remainder is calculated as 45 - (9×5) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 9 and 45 is 9.
Common Mistakes and How to Avoid Them in GCF of 9 and 45
Finding GCF of 9 and 45 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 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 indicates an incomplete understanding of the factors.
Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with 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, 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 9 and 45 Examples
Problem 1
A gardener has 9 rose plants and 45 tulip plants. She wants to arrange them into equal groups, with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 9 and 45. GCF of 9 and 45 3² = 9. There are 9 equal groups. 9 ÷ 9 = 1 45 ÷ 9 = 5 There will be 9 groups, and each group gets 1 rose plant and 5 tulip plants.
Explanation
As the GCF of 9 and 45 is 9, the gardener can make 9 groups.
Now divide 9 and 45 by 9.
Each group gets 1 rose plant and 5 tulip plants.
Problem 2
A library has 9 copies of a book and 45 copies of another. They want to arrange them in stacks with the same number of books in each stack, using the largest possible number of books per stack. How many books will be in each stack?
GCF of 9 and 45 3² = 9. So each stack will have 9 books.
Explanation
There are 9 copies of one book and 45 copies of another.
To find the total number of books in each stack, we should find the GCF of 9 and 45.
There will be 9 books in each stack.
Problem 3
A tailor has two pieces of cloth, one 9 meters long and the other 45 meters long. She wants to cut both pieces into strips of equal length, using the longest possible length. What should be the length of each strip?
For calculating the longest equal length, we have to calculate the GCF of 9 and 45. The GCF of 9 and 45 3² = 9. The strips are 9 meters long.
Explanation
For calculating the longest length of the strips, first, we need to calculate the GCF of 9 and 45, which is 9.
The length of each piece of the strip will be 9 meters.
Problem 4
A carpenter has two wooden boards, one 9 cm long and the other 45 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 45 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, 9 cm and 45 cm, respectively, we have to find the GCF of 9 and 45, 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 45, find ‘b’.
The value of ‘b’ is 45.
Explanation
GCF x LCM = product of the numbers
9 × 45
= 9 × b 405
= 9b b
= 405 ÷ 9 = 45
FAQs on the Greatest Common Factor of 9 and 45
1.What is the LCM of 9 and 45?
2.Is 9 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 45?
5.Are 9 and 45 prime numbers?
Important Glossaries for GCF of 9 and 45
- 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 45 are 3 and 5.
- 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 9 and 45 is 45.
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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.
