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GCF of 15 and 64

GCF of 15 and 64 is the largest possible number that divides 15 and 64 exactly without any remainder. The factors of 15 and 64 are 1, 3, 5, 15 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 15 and 64 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 15 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 64?

Answer: GCF of 15 and 64 is 1.

Explanation:

The GCF of two non-zero integers, x(15) and y(64), is the greatest positive integer m(1) that divides both x(15) and y(64) without any remainder.

Methods to Find GCF of 15 and 64

The methods to find the GCF of 15 and 64 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

GCF of 15 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 = 15

GCF(64, 15) = GCF(15, 64 mod 15) = GCF(15, 4)
GCF(15, 4) = GCF(4, 15 mod 4) = GCF(4, 3)
GCF(4, 3) = GCF(3, 4 mod 3) = GCF(3, 1)
GCF(3, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 15 and 64 is 1.

GCF of 15 and 64 by Prime Factorization

Prime factorization of 15 and 64 is (3 × 5) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, there are no common prime factors between 15 and 64, i.e. they are co-prime. Hence, the GCF of 15 and 64 will be 1.

GCF of 15 and 64 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 64: 1, 2, 4, 8, 16, 32, 64

Since, 1 is the only common factor between 15 and 64. The Greatest Common Factor of 15 and 64 is 1.

☛ Also Check:

GCF of 15 and 64 Examples

Example 1: Find the GCF of 15 and 64, if their LCM is 960.

Solution:

∵ LCM × GCF = 15 × 64
⇒ GCF(15, 64) = (15 × 64)/960 = 1
Therefore, the greatest common factor of 15 and 64 is 1.
Example 2: Find the greatest number that divides 15 and 64 exactly.

Solution:

The greatest number that divides 15 and 64 exactly is their greatest common factor, i.e. GCF of 15 and 64.
⇒ Factors of 15 and 64:
- Factors of 15 = 1, 3, 5, 15
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 15 and 64 is 1.
Example 3: For two numbers, GCF = 1 and LCM = 960. If one number is 15, find the other number.

Solution:

Given: GCF (x, 15) = 1 and LCM (x, 15) = 960
∵ GCF × LCM = 15 × (x)
⇒ x = (GCF × LCM)/15
⇒ x = (1 × 960)/15
⇒ x = 64
Therefore, the other number is 64.

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FAQs on GCF of 15 and 64

What is the GCF of 15 and 64?

The GCF of 15 and 64 is 1. To calculate the GCF (Greatest Common Factor) of 15 and 64, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 15 and 64, i.e., 1.

How to Find the GCF of 15 and 64 by Prime Factorization?

To find the GCF of 15 and 64, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ There is no common prime factor for 15 and 64. Hence, GCF (15, 64) = 1.
☛ Prime Numbers

If the GCF of 64 and 15 is 1, Find its LCM.

GCF(64, 15) × LCM(64, 15) = 64 × 15
Since the GCF of 64 and 15 = 1
⇒ 1 × LCM(64, 15) = 960
Therefore, LCM = 960
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 15, 64?

The following equation can be used to express the relation between LCM and GCF of 15 and 64, i.e. GCF × LCM = 15 × 64.

How to Find the GCF of 15 and 64 by Long Division Method?

To find the GCF of 15, 64 using long division method, 64 is divided by 15. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 15 and 64?

There are three commonly used methods to find the GCF of 15 and 64.

By Long Division
By Prime Factorization
By Listing Common Factors

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