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GCF of 40 and 64

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

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

What is GCF of 40 and 64?

Answer: GCF of 40 and 64 is 8.

Explanation:

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

Methods to Find GCF of 40 and 64

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

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 40 and 64 by Listing Common Factors

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

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

GCF of 40 and 64 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 64 and Y = 40

GCF(64, 40) = GCF(40, 64 mod 40) = GCF(40, 24)
GCF(40, 24) = GCF(24, 40 mod 24) = GCF(24, 16)
GCF(24, 16) = GCF(16, 24 mod 16) = GCF(16, 8)
GCF(16, 8) = GCF(8, 16 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 40 and 64 is 8.

GCF of 40 and 64 by Long Division

GCF of 40 and 64 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 40 and 64.

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GCF of 40 and 64 Examples

Example 1: Find the GCF of 40 and 64, if their LCM is 320.

Solution:

∵ LCM × GCF = 40 × 64
⇒ GCF(40, 64) = (40 × 64)/320 = 8
Therefore, the greatest common factor of 40 and 64 is 8.
Example 2: Find the greatest number that divides 40 and 64 exactly.

Solution:

The greatest number that divides 40 and 64 exactly is their greatest common factor, i.e. GCF of 40 and 64.
⇒ Factors of 40 and 64:
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 40 and 64 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 40 and 64

What is the GCF of 40 and 64?

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

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

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

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 40 and 64 by Long Division Method?

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

GCF(64, 40) × LCM(64, 40) = 64 × 40
Since the GCF of 64 and 40 = 8
⇒ 8 × LCM(64, 40) = 2560
Therefore, LCM = 320
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How to Find the GCF of 40 and 64 by Prime Factorization?

To find the GCF of 40 and 64, we will find the prime factorization of the given numbers, i.e. 40 = 2 × 2 × 2 × 5; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 40 and 64. Hence, GCF(40, 64) = 2 × 2 × 2 = 8
☛ Prime Number

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

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

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