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101 LearnersLast updated on September 24, 2025
GCF of 60 and 64
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 60 and 64.
What is the GCF of 60 and 64?
The greatest common factor of 60 and 64 is 4. 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 60 and 64?
To find the GCF of 60 and 64, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 60 and 64 by Using Listing of Factors
Steps to find the GCF of 60 and 64 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Factors of 64 = 1, 2, 4, 8, 16, 32, 64.
Step 2: Now, identify the common factors of them Common factors of 60 and 64: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 60 and 64 is 4.
GCF of 60 and 64 Using Prime Factorization
To find the GCF of 60 and 64 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 2² x 3 x 5
Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2⁶
Step 2: Now, identify the common prime factors The common prime factor is: 2 x 2 = 2²
Step 3: Multiply the common prime factors 2² = 4.
The Greatest Common Factor of 60 and 64 is 4.
GCF of 60 and 64 Using Division Method or Euclidean Algorithm Method
Find the GCF of 60 and 64 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 64 by 60 64 ÷ 60 = 1 (quotient), The remainder is calculated as 64 − (60×1) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (60) by the previous remainder (4) Divide 60 by 4 60 ÷ 4 = 15 (quotient), remainder = 60 − (4×15) = 0
The remainder is zero, so the divisor becomes the GCF. The GCF of 60 and 64 is 4.
Common Mistakes and How to Avoid Them in GCF of 60 and 64
Finding GCF of 60 and 64 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 60, students may mention 7, 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 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 60 and 64 Examples
Problem 1
A chef has 60 apples and 64 oranges. He wants to create fruit baskets with an equal number of apples and oranges in each, using the largest number possible. How many fruits will be in each basket?
We should find the GCF of 60 and 64 GCF of 60 and 64 is 4.
There will be 4 baskets, and each basket will have 15 apples and 16 oranges.
Explanation
As the GCF of 60 and 64 is 4, the chef can make 4 baskets.
Now divide 60 and 64 by 4.
Each basket gets 15 apples and 16 oranges.
Problem 2
A decorator has 60 meters of gold ribbon and 64 meters of silver ribbon. She wants to cut them 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 60 and 64.
The GCF of 60 and 64 is 4. The ribbon is cut into pieces of 4 meters each.
Explanation
To find the longest length of the ribbon pieces, first calculate the GCF of 60 and 64, which is 4. The length of each piece of ribbon will be 4 meters.
Problem 3
A builder has two wooden beams, one 60 cm long and the other 64 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 builder needs to cut the beams into the longest possible equal pieces.
The GCF of 60 and 64 is 4. The longest length of each piece is 4 cm.
Explanation
To find the longest length of each piece of the two wooden beams, 60 cm and 64 cm, respectively, find the GCF of 60 and 64, which is 4 cm. The longest length of each piece is 4 cm.
Problem 4
A gardener has 60 rose plants and 64 tulip plants. She wants to arrange them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
GCF of 60 and 64 is 4. So each row will have 4 plants.
Explanation
There are 60 rose and 64 tulip plants.
To find the total number of plants in each row, we should find the GCF of 60 and 64.
There will be 4 plants in each row.
Problem 5
If the GCF of 60 and ‘b’ is 4, and the LCM is 960. Find ‘b’.
The value of ‘b’ is 64.
Explanation
GCF x LCM = product of the numbers
4 × 960 = 60 × b
3840 = 60b
b = 3840 ÷ 60 = 64
FAQs on the Greatest Common Factor of 60 and 64
1.What is the LCM of 60 and 64?
2.Is 60 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 64?
5.Are 60 and 64 prime numbers?
Important Glossaries for GCF of 60 and 64
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 3, the remainder is 2 and the quotient is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 10 is 10.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 12 and 18 will be 6, as it is their largest common factor that divides the numbers completely.
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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.
