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GCF of 36 and 64

GCF of 36 and 64 is the largest possible number that divides 36 and 64 exactly without any remainder. The factors of 36 and 64 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 36 and 64 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 36 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 64?

Answer: GCF of 36 and 64 is 4.

Explanation:

The GCF of two non-zero integers, x(36) and y(64), is the greatest positive integer m(4) that divides both x(36) and y(64) without any remainder.

Methods to Find GCF of 36 and 64

The methods to find the GCF of 36 and 64 are explained below.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 36 and 64 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 3 common factors of 36 and 64, that are 1, 2, and 4. Therefore, the greatest common factor of 36 and 64 is 4.

GCF of 36 and 64 by Long Division

GCF of 36 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 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (28).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 36 and 64.

GCF of 36 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 = 36

GCF(64, 36) = GCF(36, 64 mod 36) = GCF(36, 28)
GCF(36, 28) = GCF(28, 36 mod 28) = GCF(28, 8)
GCF(28, 8) = GCF(8, 28 mod 8) = GCF(8, 4)
GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 64 is 4.

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GCF of 36 and 64 Examples

Example 1: Find the GCF of 36 and 64, if their LCM is 576.

Solution:

∵ LCM × GCF = 36 × 64
⇒ GCF(36, 64) = (36 × 64)/576 = 4
Therefore, the greatest common factor of 36 and 64 is 4.
Example 2: Find the greatest number that divides 36 and 64 exactly.

Solution:

The greatest number that divides 36 and 64 exactly is their greatest common factor, i.e. GCF of 36 and 64.
⇒ Factors of 36 and 64:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 36 and 64 is 4.
Example 3: For two numbers, GCF = 4 and LCM = 576. If one number is 64, find the other number.

Solution:

Given: GCF (x, 64) = 4 and LCM (x, 64) = 576
∵ GCF × LCM = 64 × (x)
⇒ x = (GCF × LCM)/64
⇒ x = (4 × 576)/64
⇒ x = 36
Therefore, the other number is 36.

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FAQs on GCF of 36 and 64

What is the GCF of 36 and 64?

The GCF of 36 and 64 is 4. To calculate the greatest common factor (GCF) of 36 and 64, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 36 and 64, i.e., 4.

If the GCF of 64 and 36 is 4, Find its LCM.

GCF(64, 36) × LCM(64, 36) = 64 × 36
Since the GCF of 64 and 36 = 4
⇒ 4 × LCM(64, 36) = 2304
Therefore, LCM = 576
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What is the Relation Between LCM and GCF of 36, 64?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 36 and 64, i.e. GCF × LCM = 36 × 64.

What are the Methods to Find GCF of 36 and 64?

There are three commonly used methods to find the GCF of 36 and 64.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 36 and 64 by Prime Factorization?

To find the GCF of 36 and 64, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 36 and 64. Hence, GCF(36, 64) = 2 × 2 = 4
☛ What is a Prime Number?

How to Find the GCF of 36 and 64 by Long Division Method?

To find the GCF of 36, 64 using long division method, 64 is divided by 36. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

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