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GCF of 16 and 32

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

1.	GCF of 16 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 32?

Answer: GCF of 16 and 32 is 16.

Explanation:

The GCF of two non-zero integers, x(16) and y(32), is the greatest positive integer m(16) that divides both x(16) and y(32) without any remainder.

Methods to Find GCF of 16 and 32

The methods to find the GCF of 16 and 32 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 16 and 32 by Listing Common Factors

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

There are 5 common factors of 16 and 32, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 16 and 32 is 16.

GCF of 16 and 32 by Prime Factorization

Prime factorization of 16 and 32 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 16 and 32 have common prime factors. Hence, the GCF of 16 and 32 is 2 × 2 × 2 × 2 = 16.

GCF of 16 and 32 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 = 32 and Y = 16

GCF(32, 16) = GCF(16, 32 mod 16) = GCF(16, 0)
GCF(16, 0) = 16 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 32 is 16.

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GCF of 16 and 32 Examples

Example 1: Find the greatest number that divides 16 and 32 exactly.

Solution:

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

Solution:

Given: GCF (y, 16) = 16 and LCM (y, 16) = 32
∵ GCF × LCM = 16 × (y)
⇒ y = (GCF × LCM)/16
⇒ y = (16 × 32)/16
⇒ y = 32
Therefore, the other number is 32.
Example 3: Find the GCF of 16 and 32, if their LCM is 32.

Solution:

∵ LCM × GCF = 16 × 32
⇒ GCF(16, 32) = (16 × 32)/32 = 16
Therefore, the greatest common factor of 16 and 32 is 16.

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FAQs on GCF of 16 and 32

What is the GCF of 16 and 32?

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

What are the Methods to Find GCF of 16 and 32?

There are three commonly used methods to find the GCF of 16 and 32.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 32 and 16 is 16, Find its LCM.

GCF(32, 16) × LCM(32, 16) = 32 × 16
Since the GCF of 32 and 16 = 16
⇒ 16 × LCM(32, 16) = 512
Therefore, LCM = 32
☛ Greatest Common Factor Calculator

How to Find the GCF of 16 and 32 by Prime Factorization?

To find the GCF of 16 and 32, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 16 and 32. Hence, GCF(16, 32) = 2 × 2 × 2 × 2 = 16
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 16, 32?

The following equation can be used to express the relation between LCM and GCF of 16 and 32, i.e. GCF × LCM = 16 × 32.

How to Find the GCF of 16 and 32 by Long Division Method?

To find the GCF of 16, 32 using long division method, 32 is divided by 16. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

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