Gcf Of 30 And 16

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 one, 2, 4, 8, 16 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the GCF of xvi and 32 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 16 and 32
two.	List of Methods
three.	Solved Examples
4.	FAQs

What is GCF of 16 and 32?

Answer: GCF of 16 and 32 is 16.

GCF of 16 and 32

Explanation:

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

Methods to Find GCF of 16 and 32

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

Listing Mutual Factors
Prime number Factorization Method
Using Euclid'south Algorithm

GCF of xvi and 32 by Listing Common Factors

GCF of 16 and 32 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, xvi
Factors of 32: i, 2, iv, viii, 16, 32

There are v common factors of 16 and 32, that are 1, 2, 4, 8, and 16. Therefore, the greatest common gene of sixteen and 32 is 16.

GCF of xvi and 32 by Prime number Factorization

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, xvi and 32 have common prime factors. Hence, the GCF of 16 and 32 is 2 × 2 × 2 × two = xvi.

GCF of 16 and 32 past Euclidean Algorithm

As per the Euclidean Algorithm, GCF(Ten, Y) = GCF(Y, X modernistic Y)
where X > Y and mod is the modulo operator.

Here Ten = 32 and Y = 16

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

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

☛ Also Check:

GCF of vii and 28 = 7
GCF of two and 6 = 2
GCF of 24 and 72 = 24
GCF of 25 and sixty = 5
GCF of 55 and 77 = 11
GCF of 28 and 56 = 28
GCF of 64 and 80 = 16

GCF of xvi and 32 Examples

Case one: Find the greatest number that divides sixteen and 32 exactly.

Solution:

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

Solution:

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

Solution:

∵ LCM × GCF = xvi × 32
⇒ GCF(xvi, 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 xvi and 32 is sixteen . To calculate the greatest common factor (GCF) of 16 and 32, we need to factor each number (factors of sixteen = 1, two, 4, viii, sixteen; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 16 and 32, i.e., sixteen.

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 xvi is 16, Find its LCM.

GCF(32, xvi) × LCM(32, 16) = 32 × xvi
Since the GCF of 32 and sixteen = 16
⇒ xvi × LCM(32, 16) = 512
Therefore, LCM = 32
☛ Greatest Common Gene Estimator

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

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

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

The following equation can exist 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 past Long Division Method?

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