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GCF of 64 and 40

GCF of 64 and 40 is the largest possible number that divides 64 and 40 exactly without any remainder. The factors of 64 and 40 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 64 and 40 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 64 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 64 and 40?

Answer: GCF of 64 and 40 is 8.

Explanation:

The GCF of two non-zero integers, x(64) and y(40), is the greatest positive integer m(8) that divides both x(64) and y(40) without any remainder.

Methods to Find GCF of 64 and 40

The methods to find the GCF of 64 and 40 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 64 and 40 by Listing Common Factors

Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 4 common factors of 64 and 40, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 64 and 40 is 8.

GCF of 64 and 40 by Long Division

GCF of 64 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 64 (larger number) by 40 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (40) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 64 and 40.

GCF of 64 and 40 by Prime Factorization

Prime factorization of 64 and 40 is (2 × 2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 5) respectively. As visible, 64 and 40 have common prime factors. Hence, the GCF of 64 and 40 is 2 × 2 × 2 = 8.

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GCF of 64 and 40 Examples

Example 1: The product of two numbers is 2560. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 2560
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2560/8
Therefore, the LCM is 320.
Example 2: Find the GCF of 64 and 40, if their LCM is 320.

Solution:

∵ LCM × GCF = 64 × 40
⇒ GCF(64, 40) = (64 × 40)/320 = 8
Therefore, the greatest common factor of 64 and 40 is 8.
Example 3: For two numbers, GCF = 8 and LCM = 320. If one number is 64, find the other number.

Solution:

Given: GCF (z, 64) = 8 and LCM (z, 64) = 320
∵ GCF × LCM = 64 × (z)
⇒ z = (GCF × LCM)/64
⇒ z = (8 × 320)/64
⇒ z = 40
Therefore, the other number is 40.

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FAQs on GCF of 64 and 40

What is the GCF of 64 and 40?

The GCF of 64 and 40 is 8. To calculate the GCF (Greatest Common Factor) of 64 and 40, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 64 and 40, i.e., 8.

What are the Methods to Find GCF of 64 and 40?

There are three commonly used methods to find the GCF of 64 and 40.

By Listing Common Factors
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 64, 40?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 64 and 40, i.e. GCF × LCM = 64 × 40.

How to Find the GCF of 64 and 40 by Prime Factorization?

To find the GCF of 64 and 40, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 64 and 40. Hence, GCF(64, 40) = 2 × 2 × 2 = 8
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How to Find the GCF of 64 and 40 by Long Division Method?

To find the GCF of 64, 40 using long division method, 64 is divided by 40. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

If the GCF of 40 and 64 is 8, Find its LCM.

GCF(40, 64) × LCM(40, 64) = 40 × 64
Since the GCF of 40 and 64 = 8
⇒ 8 × LCM(40, 64) = 2560
Therefore, LCM = 320
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