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GCF of 27 and 64

GCF of 27 and 64 is the largest possible number that divides 27 and 64 exactly without any remainder. The factors of 27 and 64 are 1, 3, 9, 27 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 27 and 64 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 27 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 64?

Answer: GCF of 27 and 64 is 1.

Explanation:

The GCF of two non-zero integers, x(27) and y(64), is the greatest positive integer m(1) that divides both x(27) and y(64) without any remainder.

Methods to Find GCF of 27 and 64

The methods to find the GCF of 27 and 64 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 27 and 64 by Prime Factorization

Prime factorization of 27 and 64 is (3 × 3 × 3) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, there are no common prime factors between 27 and 64, i.e. they are coprime. Hence, the GCF of 27 and 64 will be 1.

GCF of 27 and 64 by Long Division

GCF of 27 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 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 27 and 64.

GCF of 27 and 64 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 64: 1, 2, 4, 8, 16, 32, 64

Since, 1 is the only common factor between 27 and 64. The Greatest Common Factor of 27 and 64 is 1.

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GCF of 27 and 64 Examples

Example 1: The product of two numbers is 1728. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 1728
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1728/1
Therefore, the LCM is 1728.
Example 2: For two numbers, GCF = 1 and LCM = 1728. If one number is 27, find the other number.

Solution:

Given: GCF (x, 27) = 1 and LCM (x, 27) = 1728
∵ GCF × LCM = 27 × (x)
⇒ x = (GCF × LCM)/27
⇒ x = (1 × 1728)/27
⇒ x = 64
Therefore, the other number is 64.
Example 3: Find the greatest number that divides 27 and 64 exactly.

Solution:

The greatest number that divides 27 and 64 exactly is their greatest common factor, i.e. GCF of 27 and 64.
⇒ Factors of 27 and 64:
- Factors of 27 = 1, 3, 9, 27
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 27 and 64 is 1.

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FAQs on GCF of 27 and 64

What is the GCF of 27 and 64?

The GCF of 27 and 64 is 1. To calculate the GCF of 27 and 64, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 27 and 64, i.e., 1.

If the GCF of 64 and 27 is 1, Find its LCM.

GCF(64, 27) × LCM(64, 27) = 64 × 27
Since the GCF of 64 and 27 = 1
⇒ 1 × LCM(64, 27) = 1728
Therefore, LCM = 1728
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How to Find the GCF of 27 and 64 by Long Division Method?

To find the GCF of 27, 64 using long division method, 64 is divided by 27. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 27, 64?

The following equation can be used to express the relation between Least Common Multiple and GCF of 27 and 64, i.e. GCF × LCM = 27 × 64.

What are the Methods to Find GCF of 27 and 64?

There are three commonly used methods to find the GCF of 27 and 64.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 27 and 64 by Prime Factorization?

To find the GCF of 27 and 64, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ There is no common prime factor for 27 and 64. Hence, GCF (27, 64) = 1.
☛ What is a Prime Number?

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