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104 LearnersLast updated on September 24, 2025
GCF of 645 and 180
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 645 and 180.
What is the GCF of 645 and 180?
The greatest common factor of 645 and 180 is 15. 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 645 and 180?
To find the GCF of 645 and 180, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 645 and 180 by Using Listing of Factors
Steps to find the GCF of 645 and 180 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 645 = 1, 3, 5, 15, 43, 129, 215, 645.
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Step 2: Now, identify the common factors of them Common factors of 645 and 180: 1, 3, 5, 15.
Step 3: Choose the largest factor The largest factor that both numbers have is 15.
The GCF of 645 and 180 is 15.
GCF of 645 and 180 Using Prime Factorization
To find the GCF of 645 and 180 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 645: 645 = 3 x 5 x 43
Prime Factors of 180: 180 = 2 x 2 x 3 x 3 x 5
Step 2: Now, identify the common prime factors The common prime factors are: 3 x 5
Step 3: Multiply the common prime factors 3 x 5 = 15.
The Greatest Common Factor of 645 and 180 is 15.
GCF of 645 and 180 Using Division Method or Euclidean Algorithm Method
Find the GCF of 645 and 180 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 645 by 180 645 ÷ 180 = 3 (quotient),
The remainder is calculated as 645 − (180×3) = 105
The remainder is 105, not zero, so continue the process
Step 2: Now divide the previous divisor (180) by the previous remainder (105)
Divide 180 by 105 180 ÷ 105 = 1 (quotient), remainder = 180 − (105×1) = 75
Step 3: Divide the previous divisor (105) by the previous remainder (75)
Divide 105 by 75 105 ÷ 75 = 1 (quotient), remainder = 105 − (75×1) = 30
Step 4: Divide the previous divisor (75) by the previous remainder (30) 75 ÷ 30 = 2 (quotient), remainder = 75 − (30×2) = 15
Step 5: Divide the previous divisor (30) by the previous remainder (15) 30 ÷ 15 = 2 (quotient), remainder = 30 − (15×2) = 0 The remainder is zero, the divisor will become the GCF.
The GCF of 645 and 180 is 15.
Common Mistakes and How to Avoid Them in GCF of 645 and 180
Finding GCF of 645 and 180 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 645, students may mention 2 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 645 and 180 Examples
Problem 1
A gardener has 645 tulip bulbs and 180 daffodil bulbs. She wants to plant them in equal sections, with the largest number of bulbs in each section. How many bulbs will be in each section?
We should find the GCF of 645 and 180 GCF of 645 and 180 3 x 5 = 15.
There are 15 equal sections 645 ÷ 15 = 43 180 ÷ 15 = 12
There will be 15 sections, and each section gets 43 tulip bulbs and 12 daffodil bulbs.
Explanation
As the GCF of 645 and 180 is 15, the gardener can make 15 sections.
Now divide 645 and 180 by 15.
Each section gets 43 tulip bulbs and 12 daffodil bulbs.
Problem 2
A shipping company has 645 large boxes and 180 small boxes. They want to arrange them in stacks with the same number of boxes in each stack, using the largest possible number of boxes per stack. How many boxes will be in each stack?
GCF of 645 and 180 3 x 5 = 15.
So each stack will have 15 boxes.
Explanation
There are 645 large and 180 small boxes. To find the total number of boxes in each stack, we should find the GCF of 645 and 180. There will be 15 boxes in each stack.
Problem 3
A tailor has 645 meters of red fabric and 180 meters of blue 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 645 and 180
The GCF of 645 and 180 3 x 5 = 15.
The fabric is 15 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 645 and 180 which is 15.
The length of each piece of the fabric will be 15 meters.
Problem 4
A carpenter has two wooden planks, one 645 cm long and the other 180 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 645 and 180 3 x 5 = 15.
The longest length of each piece is 15 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 645 cm and 180 cm, respectively.
We have to find the GCF of 645 and 180, which is 15 cm.
The longest length of each piece is 15 cm.
Problem 5
If the GCF of 645 and ‘a’ is 15, and the LCM is 7740. Find ‘a’.
The value of ‘a’ is 180.
Explanation
GCF x LCM = product of the numbers
15 × 7740 = 645 × a
116100 = 645a
a = 116100 ÷ 645 = 180
FAQs on the Greatest Common Factor of 645 and 180
1.What is the LCM of 645 and 180?
2.Is 645 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 180?
5.Are 645 and 180 prime numbers?
Important Glossaries for GCF of 645 and 180
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 15 are 1, 3, 5, and 15.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 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 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 10 is 10.
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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.
