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102 LearnersLast updated on September 18, 2025
GCF of 64 and 144
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 schedule events. In this topic, we will learn about the GCF of 64 and 144.
What is the GCF of 64 and 144?
The greatest common factor of 64 and 144 is 16. 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 64 and 144?
To find the GCF of 64 and 144, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 64 and 144 by Using Listing of Factors
Steps to find the GCF of 64 and 144 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 64 = 1, 2, 4, 8, 16, 32, 64.
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 64 and 144: 1, 2, 4, 8, 16.
Step 3: Choose the largest factor The largest factor that both numbers have is 16.
The GCF of 64 and 144 is 16.
GCF of 64 and 144 Using Prime Factorization
To find the GCF of 64 and 144 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 64: 64 = 2 × 2 × 2 × 2 × 2 × 2 = 26
Prime Factors of 144: 144 = 2 × 2 × 2 × 2 × 3 × 3 = 24 × 32
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 2 × 2 = 24
Step 3: Multiply the common prime factors 2^4 = 16.
The Greatest Common Factor of 64 and 144 is 16.
GCF of 64 and 144 Using Division Method or Euclidean Algorithm Method
Find the GCF of 64 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 64 144 ÷ 64 = 2 (quotient),
The remainder is calculated as 144 − (64×2) = 16
The remainder is 16, not zero, so continue the process
Step 2: Now divide the previous divisor (64) by the previous remainder (16) Divide 64 by 16 64 ÷ 16 = 4 (quotient), remainder = 64 − (16×4) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 64 and 144 is 16.
Common Mistakes and How to Avoid Them in GCF of 64 and 144
Finding the GCF of 64 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 64, 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 indicates an 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 64 and 144 Examples
Problem 1
A gardener has 64 roses and 144 tulips. She wants to create bouquets with the same number of flowers in each, using the largest possible number of flowers per bouquet. How many flowers will be in each bouquet?
We should find the GCF of 64 and 144 GCF of 64 and 144 24 = 16.
There are 16 equal bouquets 64 ÷ 16 = 4 144 ÷ 16 = 9
There will be 16 bouquets, and each bouquet gets 4 roses and 9 tulips.
Explanation
As the GCF of 64 and 144 is 16, the gardener can make 16 bouquets.
Now divide 64 and 144 by 16.
Each bouquet gets 4 roses and 9 tulips.
Problem 2
A construction company has 64 bricks and 144 tiles. They want to arrange them in stacks with the same number of items in each stack, using the largest possible number of items per stack. How many items will be in each stack?
GCF of 64 and 144 24 = 16. So each stack will have 16 items.
Explanation
There are 64 bricks and 144 tiles.
To find the total number of items in each stack, we should find the GCF of 64 and 144.
There will be 16 items in each stack.
Problem 3
A tailor has 64 meters of red fabric and 144 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 64 and 144
The GCF of 64 and 144
24 = 16.
The fabric is 16 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 64 and 144, which is 16.
The length of each piece of fabric will be 16 meters.
Problem 4
A carpenter has two wooden planks, one 64 cm long and the other 144 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 64 and 144
24 = 16.
The longest length of each piece is 16 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 64 cm and 144 cm, respectively, we have to find the GCF of 64 and 144, which is 16 cm.
The longest length of each piece is 16 cm.
Problem 5
If the GCF of 64 and ‘b’ is 16, and the LCM is 576, find ‘b’.
The value of ‘b’ is 144.
Explanation
GCF × LCM = product of the numbers
16 × 576 = 64 × b
9216 = 64b
b = 9216 ÷ 64 = 144
FAQs on the Greatest Common Factor of 64 and 144
1.What is the LCM of 64 and 144?
2.Is 64 divisible by 4?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 144?
5.Are 64 and 144 prime numbers?
Important Glossaries for GCF of 64 and 144
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 16 are 1, 2, 4, 8, and 16.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, 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 64 are 2 × 2 × 2 × 2 × 2 × 2.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 4, the remainder is 1 and the quotient is 6.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 64 and 144 is 576.
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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.
