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GCF of 16 and 64

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

1.	GCF of 16 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 64?

Answer: GCF of 16 and 64 is 16.

Explanation:

The GCF of two non-zero integers, x(16) and y(64), is the greatest positive integer m(16) that divides both x(16) and y(64) without any remainder.

Methods to Find GCF of 16 and 64

Let's look at the different methods for finding the GCF of 16 and 64.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 16 and 64 by Long Division

GCF of 16 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 16 (smaller number).
Step 2: Since the remainder = 0, the divisor (16) is the GCF of 16 and 64.

The corresponding divisor (16) is the GCF of 16 and 64.

GCF of 16 and 64 by Prime Factorization

Prime factorization of 16 and 64 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 16 and 64 have common prime factors. Hence, the GCF of 16 and 64 is 2 × 2 × 2 × 2 = 16.

GCF of 16 and 64 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 5 common factors of 16 and 64, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 16 and 64 is 16.

☛ Also Check:

GCF of 16 and 64 Examples

Example 1: Find the greatest number that divides 16 and 64 exactly.

Solution:

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

Solution:

Given: GCF (x, 64) = 16 and LCM (x, 64) = 64
∵ GCF × LCM = 64 × (x)
⇒ x = (GCF × LCM)/64
⇒ x = (16 × 64)/64
⇒ x = 16
Therefore, the other number is 16.
Example 3: Find the GCF of 16 and 64, if their LCM is 64.

Solution:

∵ LCM × GCF = 16 × 64
⇒ GCF(16, 64) = (16 × 64)/64 = 16
Therefore, the greatest common factor of 16 and 64 is 16.

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FAQs on GCF of 16 and 64

What is the GCF of 16 and 64?

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

What is the Relation Between LCM and GCF of 16, 64?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 16 and 64, i.e. GCF × LCM = 16 × 64.

How to Find the GCF of 16 and 64 by Long Division Method?

To find the GCF of 16, 64 using long division method, 64 is divided by 16. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 16 and 64?

There are three commonly used methods to find the GCF of 16 and 64.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 16 and 64 by Prime Factorization?

To find the GCF of 16 and 64, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 16 and 64. Hence, GCF(16, 64) = 2 × 2 × 2 × 2 = 16
☛ Prime Numbers

If the GCF of 64 and 16 is 16, Find its LCM.

GCF(64, 16) × LCM(64, 16) = 64 × 16
Since the GCF of 64 and 16 = 16
⇒ 16 × LCM(64, 16) = 1024
Therefore, LCM = 64
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