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104 LearnersLast updated on September 24, 2025
GCF of 36 and 144
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 36 and 144.
What is the GCF of 36 and 144?
The greatest common factor of 36 and 144 is 36. 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 36 and 144?
To find the GCF of 36 and 144, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 36 and 144 by Using Listing of Factors
Steps to find the GCF of 36 and 144 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144.
Step 2: Now, identify the common factors of them Common factors of 36 and 144: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 3: Choose the largest factor The largest factor that both numbers have is 36. The GCF of 36 and 144 is 36.
GCF of 36 and 144 Using Prime Factorization
To find the GCF of 36 and 144 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²
Prime Factors of 144: 144 = 2 x 2 x 2 x 2 x 3 x 3 = 2⁴ x 3²
Step 2: Now, identify the common prime factors The common prime factors are: 2² x 3²
Step 3: Multiply the common prime factors 2² x 3² = 4 x 9 = 36.
The Greatest Common Factor of 36 and 144 is 36.
GCF of 36 and 144 Using Division Method or Euclidean Algorithm Method
Find the GCF of 36 and 144 using the division method or Euclidean Algorithm Method.
Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 144 by 36 144 ÷ 36 = 4 (quotient), The remainder is calculated as 144 − (36 x 4) = 0
The remainder is zero, so the divisor becomes the GCF. The GCF of 36 and 144 is 36.
Common Mistakes and How to Avoid Them in GCF of 36 and 144
Finding the GCF of 36 and 144 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 144, 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 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; 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 36 and 144 Examples
Problem 1
A gardener has 36 roses and 144 tulips. She wants to arrange them into bouquets, each with an equal number of flowers. What is the maximum number of flowers each bouquet can have?
We should find the GCF of 36 and 144 GCF of 36 and 144 2² x 3² = 4 x 9 = 36.
There will be 36 flowers in each bouquet.
Explanation
As the GCF of 36 and 144 is 36, the gardener can arrange the flowers into bouquets with 36 flowers each.
Problem 2
A decorator has 36 red ribbons and 144 blue ribbons. She wants to cut them into pieces of equal length, using the longest possible length. What should be the length of each piece?
GCF of 36 and 144 2² x 3² = 4 x 9 = 36.
So, each piece will be 36 units long.
Explanation
There are 36 red and 144 blue ribbons.
To find the length of each piece, we should find the GCF of 36 and 144.
Each piece will be 36 units long.
Problem 3
A contractor has two metal rods, one 36 cm long and the other 144 cm long. He wants to cut them into the longest possible equal pieces without any metal left over. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 36 and 144
The GCF of 36 and 144 2² x 3² = 4 x 9 = 36.
The length of each piece is 36 cm.
Explanation
For calculating the longest length of the rods, first, we need to calculate the GCF of 36 and 144, which is 36.
The length of each piece will be 36 cm.
Problem 4
A chef has 36 eggs and 144 grams of flour. He wants to make cakes with the largest possible number of eggs and flour per cake. How many eggs and grams of flour will each cake have?
The chef needs the largest ratio of eggs to flour GCF of 36 and 144 2² x 3² = 4 x 9 = 36.
Each cake will have 36 eggs and 36 grams of flour.
Explanation
To find the maximum number of eggs and flour per cake, we have to find the GCF of 36 and 144, which is 36. Each cake will have 36 eggs and 36 grams of flour.
Problem 5
If the GCF of 36 and ‘b’ is 36, and the LCM is 144, find ‘b’.
The value of ‘b’ is 144.
Explanation
GCF x LCM = product of the numbers
36 x 144 = 36 x b
b = 144
FAQs on the Greatest Common Factor of 36 and 144
1.What is the LCM of 36 and 144?
2.Is 36 divisible by 3?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 144?
5.Are 36 and 144 prime numbers?
Important Glossaries for GCF of 36 and 144
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- 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 36 are 2 and 3.
- Divisor: A divisor is a number that divides another number completely, leaving no remainder. For example, 6 is a divisor of 36.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 38 is divided by 6, the remainder is 2.
- Euclidean Algorithm: A method for finding the GCF of two numbers by repeatedly applying the division algorithm.
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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.
