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104 LearnersLast updated on September 22, 2025
GCF of 64 and 88
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 to schedule events. In this topic, we will learn about the GCF of 64 and 88.
What is the GCF of 64 and 88?
The greatest common factor of 64 and 88 is 8. 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 64 and 88?
To find the GCF of 64 and 88, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 64 and 88 by Using Listing of factors
Steps to find the GCF of 64 and 88 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 88 = 1, 2, 4, 8, 11, 22, 44, 88.
Step 2: Now, identify the common factors of them Common factors of 64 and 88: 1, 2, 4, 8.
Step 3: Choose the largest factor The largest factor that both numbers have is 8.
The GCF of 64 and 88 is 8.
GCF of 64 and 88 Using Prime Factorization
To find the GCF of 64 and 88 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 64: 64 = 2 x 2 x 2 x 2 x 2 x 2 = 26
Prime Factors of 88: 88 = 2 x 2 x 2 x 11 = 23 x 11
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 = 23
Step 3: Multiply the common prime factors 23 = 8
The Greatest Common Factor of 64 and 88 is 8.
GCF of 64 and 88 Using Division Method or Euclidean Algorithm Method
Find the GCF of 64 and 88 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 88 by 64 88 ÷ 64 = 1 (quotient),
The remainder is calculated as 88 − (64×1) = 24
The remainder is 24, not zero, so continue the process
Step 2: Now divide the previous divisor (64) by the previous remainder (24)
Divide 64 by 24 64 ÷ 24 = 2 (quotient), remainder = 64 − (24×2) = 16
Step 3: Continue the process with the new divisor (24) and the new remainder (16)
Divide 24 by 16 24 ÷ 16 = 1 (quotient), remainder = 24 − (16×1) = 8
Finally, divide 16 by 8 16 ÷ 8 = 2 (quotient), remainder = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 64 and 88 is 8.
Common Mistakes and How to Avoid Them in GCF of 64 and 88
Finding the GCF of 64 and 88 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 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 88 Examples
Problem 1
A gardener has 64 tulips and 88 daffodils. She wants to plant them in the largest possible equal groups. How many flowers will be in each group?
We should find the GCF of 64 and 88 GCF of 64 and 88 23 = 8
There are 8 equal groups 64 ÷ 8 = 8 88 ÷ 8 = 11
There will be 8 groups, and each group gets 8 tulips and 11 daffodils.
Explanation
As the GCF of 64 and 88 is 8, the gardener can make 8 groups.
Now divide 64 and 88 by 8.
Each group gets 8 tulips and 11 daffodils.
Problem 2
A book club has 64 mystery novels and 88 science fiction novels. They want to organize them into shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be on each shelf?
GCF of 64 and 88 23 = 8
So each shelf will have 8 books.
Explanation
There are 64 mystery novels and 88 science fiction novels.
To find the total number of books on each shelf, we should find the GCF of 64 and 88.
There will be 8 books on each shelf.
Problem 3
A tailor has 64 meters of silk and 88 meters of cotton. 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 88
The GCF of 64 and 88 23 = 8
The fabric is 8 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 64 and 88, which is 8.
The length of each piece of fabric will be 8 meters.
Problem 4
A carpenter has two wooden planks, one 64 cm long and the other 88 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 88 23 = 8
The longest length of each piece is 8 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 64 cm and 88 cm respectively, we have to find the GCF of 64 and 88, which is 8 cm.
The longest length of each piece is 8 cm.
Problem 5
If the GCF of 64 and ‘a’ is 8, and the LCM is 704. Find ‘a’.
The value of ‘a’ is 88.
Explanation
GCF x LCM = product of the numbers
8 × 704 = 64 × a
5632 = 64a
a = 5632 ÷ 64 = 88
FAQs on the Greatest Common Factor of 64 and 88
1.What is the LCM of 64 and 88?
2.Is 64 divisible by 4?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 88?
5.Are 64 and 88 prime numbers?
Important Glossaries for GCF of 64 and 88
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Prime Factorization: Breaking down a number into its basic building blocks, which are prime numbers. For example, the prime factorization of 64 is 26.
- Divisor: A number that divides another number completely without leaving a remainder. For example, 8 is a divisor of 64.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 88 is divided by 64, the remainder is 24.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 64 and 88 is 704.
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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.
