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102 LearnersLast updated on September 9, 2025
GCF of 64 and 40
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 64 and 40.
What is the GCF of 64 and 40?
The greatest common factor of 64 and 40 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 40?
To find the GCF of 64 and 40, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 64 and 40 by Using Listing of factors
Steps to find the GCF of 64 and 40 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 40 = 1, 2, 4, 5, 8, 10, 20, 40.
Step 2: Now, identify the common factors of them Common factors of 64 and 40: 1, 2, 4, 8.
Step 3: Choose the largest factor The largest factor that both numbers have is 8. The GCF of 64 and 40 is 8.
GCF of 64 and 40 Using Prime Factorization
To find the GCF of 64 and 40 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 = 2^6Prime Factors of 40: 40 = 2 x 2 x 2 x 5 = 2^3 x 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 2 = 2^3
Step 3: Multiply the common prime factors 2^3 = 8. The Greatest Common Factor of 64 and 40 is 8.
GCF of 64 and 40 Using Division Method or Euclidean Algorithm Method
Find the GCF of 64 and 40 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 40 64 ÷ 40 = 1 (quotient), The remainder is calculated as 64 − (40×1) = 24 The remainder is 24, not zero, so continue the process
Step 2: Now divide the previous divisor (40) by the previous remainder (24) Divide 40 by 24 40 ÷ 24 = 1 (quotient), remainder = 40 − (24×1) = 16
Step 3: Continue the process: Divide 24 by 16 24 ÷ 16 = 1 (quotient), remainder = 24 − (16×1) = 8 Now, divide 16 by 8 16 ÷ 8 = 2 (quotient), remainder = 16 − (8×2) = 0 The remainder is zero, the divisor will become the GCF. The GCF of 64 and 40 is 8.
Common Mistakes and How to Avoid Them in GCF of 64 and 40
Finding GCF of 64 and 40 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 12 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 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 64 and 40 Examples
Problem 1
A gardener has 64 rose bushes and 40 lilac bushes. She wants to plant them in rows with the largest number of bushes in each row, ensuring each row has the same number of bushes. How many bushes will be in each row?
We should find the GCF of 64 and 40 GCF of 64 and 40 2^3 = 8. There are 8 bushes per row. 64 ÷ 8 = 8 rows 40 ÷ 8 = 5 rows There will be 8 rows, and each row will have 8 bushes.
Explanation
As the GCF of 64 and 40 is 8, the gardener can make 8 rows.
Now divide 64 and 40 by 8.
Each row gets 8 bushes.
Problem 2
A decorator has 64 meters of red fabric and 40 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?
GCF of 64 and 40 2^3 = 8. So each piece will be 8 meters long.
Explanation
There are 64 meters of red fabric and 40 meters of blue fabric.
To find the longest possible equal length, we should find the GCF of 64 and 40.
Each piece will be 8 meters long.
Problem 3
A chef has 64 apples and 40 oranges. He wants to divide them into fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits. How many fruits will be in each basket?
For calculating the largest number of fruits in each basket, we have to calculate the GCF of 64 and 40 The GCF of 64 and 40 2^3 = 8. Each basket will have 8 fruits.
Explanation
For calculating the largest number of fruits in each basket, first we need to calculate the GCF of 64 and 40, which is 8. Each basket will have 8 fruits.
Problem 4
A carpenter has two wooden planks, one 64 cm long and the other 40 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 40 2^3 = 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 40 cm, respectively. We have to find the GCF of 64 and 40, which is 8 cm.
The longest length of each piece is 8 cm.
Problem 5
If the GCF of 64 and ‘b’ is 8, and the LCM is 320. Find ‘b’.
The value of ‘b’ is 40.
Explanation
GCF x LCM = product of the numbers
8 × 320
= 64 × b 2560
= 64b b
= 2560 ÷ 64 = 40
FAQs on the Greatest Common Factor of 64 and 40
1.What is the LCM of 64 and 40?
2.Is 64 divisible by 4?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 40?
5.Are 64 and 40 prime numbers?
Important Glossaries for GCF of 64 and 40
- 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 40 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 64 and 40 is 320.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 64 and 40 is 8, 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.
