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102 LearnersLast updated on September 9, 2025
GCF of 45 and 81
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 45 and 81.
What is the GCF of 45 and 81?
The greatest common factor of 45 and 81 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 45 and 81?
To find the GCF of 45 and 81, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 45 and 81 by Using Listing of Factors
Steps to find the GCF of 45 and 81 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 45 = 1, 3, 5, 9, 15, 45. Factors of 81 = 1, 3, 9, 27, 81.
Step 2: Now, identify the common factors of them Common factors of 45 and 81: 1, 3, 9.
Step 3: Choose the largest factor The largest factor that both numbers have is 9. The GCF of 45 and 81 is 9.
GCF of 45 and 81 Using Prime Factorization
To find the GCF of 45 and 81 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 45: 45 = 3 × 3 × 5 = 3² × 5 Prime Factors of 81: 81 = 3 × 3 × 3 × 3 = 3⁴
Step 2: Now, identify the common prime factors The common prime factors are: 3 × 3 = 3²
Step 3: Multiply the common prime factors 3² = 9. The Greatest Common Factor of 45 and 81 is 9.
GCF of 45 and 81 Using Division Method or Euclidean Algorithm Method
Find the GCF of 45 and 81 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 81 by 45 81 ÷ 45 = 1 (quotient), The remainder is calculated as 81 − (45×1) = 36 The remainder is 36, not zero, so continue the process
Step 2: Now divide the previous divisor (45) by the previous remainder (36) Divide 45 by 36 45 ÷ 36 = 1 (quotient), remainder = 45 − (36×1) = 9 The remainder is 9, not zero, so continue the process
Step 3: Now divide the previous divisor (36) by the previous remainder (9) Divide 36 by 9 36 ÷ 9 = 4 (quotient), remainder = 36 − (9×4) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 45 and 81 is 9.
Common Mistakes and How to Avoid Them in GCF of 45 and 81
Finding GCF of 45 and 81 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 45, students may mention 10 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 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 45 and 81 Examples
Problem 1
A teacher has 45 notebooks and 81 markers. 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 45 and 81 GCF of 45 and 81 3² = 9. There are 9 equal groups 45 ÷ 9 = 5 81 ÷ 9 = 9 There will be 9 groups, and each group gets 5 notebooks and 9 markers.
Explanation
As the GCF of 45 and 81 is 9, the teacher can make 9 groups.
Now divide 45 and 81 by 9.
Each group gets 5 notebooks and 9 markers.
Problem 2
A school has 45 red chairs and 81 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 45 and 81 3² = 9. So each row will have 9 chairs.
Explanation
There are 45 red and 81 blue chairs.
To find the total number of chairs in each row, we should find the GCF of 45 and 81.
There will be 9 chairs in each row.
Problem 3
A tailor has 45 meters of red ribbon and 81 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 45 and 81 The GCF of 45 and 81 3² = 9. The ribbon is 9 meters long.
Explanation
For calculating the longest length of the ribbon first we need to calculate the GCF of 45 and 81 which is 9.
The length of each piece of the ribbon will be 9 meters.
Problem 4
A carpenter has two wooden planks, one 45 cm long and the other 81 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 45 and 81 3² = 9. The longest length of each piece is 9 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 45 cm and 81 cm, respectively.
We have to find the GCF of 45 and 81, which is 9 cm.
The longest length of each piece is 9 cm.
Problem 5
If the GCF of 45 and ‘a’ is 9, and the LCM is 405. Find ‘a’.
The value of ‘a’ is 81.
Explanation
GCF × LCM = product of the numbers
9 × 405
= 45 × a 3645
= 45a a
= 3645 ÷ 45 = 81
FAQs on the Greatest Common Factor of 45 and 81
1.What is the LCM of 45 and 81?
2.Is 45 divisible by 3?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 81?
5.Are 45 and 81 prime numbers?
Important Glossaries for GCF of 45 and 81
- 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, 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 15 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 45 and 81 is 405.
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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.
