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GCF of 16 and 30

GCF of 16 and 30 is the largest possible number that divides 16 and 30 exactly without any remainder. The factors of 16 and 30 are 1, 2, 4, 8, 16 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 16 and 30 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 16 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 30?

Answer: GCF of 16 and 30 is 2.

Explanation:

The GCF of two non-zero integers, x(16) and y(30), is the greatest positive integer m(2) that divides both x(16) and y(30) without any remainder.

Methods to Find GCF of 16 and 30

The methods to find the GCF of 16 and 30 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 16 and 30 by Long Division

GCF of 16 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (14).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 16 and 30.

GCF of 16 and 30 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 = 30 and Y = 16

GCF(30, 16) = GCF(16, 30 mod 16) = GCF(16, 14)
GCF(16, 14) = GCF(14, 16 mod 14) = GCF(14, 2)
GCF(14, 2) = GCF(2, 14 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 30 is 2.

GCF of 16 and 30 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 2 common factors of 16 and 30, that are 1 and 2. Therefore, the greatest common factor of 16 and 30 is 2.

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GCF of 16 and 30 Examples

Example 1: Find the GCF of 16 and 30, if their LCM is 240.

Solution:

∵ LCM × GCF = 16 × 30
⇒ GCF(16, 30) = (16 × 30)/240 = 2
Therefore, the greatest common factor of 16 and 30 is 2.
Example 2: Find the greatest number that divides 16 and 30 exactly.

Solution:

The greatest number that divides 16 and 30 exactly is their greatest common factor, i.e. GCF of 16 and 30.
⇒ Factors of 16 and 30:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 16 and 30 is 2.
Example 3: For two numbers, GCF = 2 and LCM = 240. If one number is 30, find the other number.

Solution:

Given: GCF (x, 30) = 2 and LCM (x, 30) = 240
∵ GCF × LCM = 30 × (x)
⇒ x = (GCF × LCM)/30
⇒ x = (2 × 240)/30
⇒ x = 16
Therefore, the other number is 16.

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FAQs on GCF of 16 and 30

What is the GCF of 16 and 30?

The GCF of 16 and 30 is 2. To calculate the GCF (Greatest Common Factor) of 16 and 30, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 16 and 30, i.e., 2.

How to Find the GCF of 16 and 30 by Long Division Method?

To find the GCF of 16, 30 using long division method, 30 is divided by 16. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 16, 30?

The following equation can be used to express the relation between Least Common Multiple and GCF of 16 and 30, i.e. GCF × LCM = 16 × 30.

If the GCF of 30 and 16 is 2, Find its LCM.

GCF(30, 16) × LCM(30, 16) = 30 × 16
Since the GCF of 30 and 16 = 2
⇒ 2 × LCM(30, 16) = 480
Therefore, LCM = 240
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What are the Methods to Find GCF of 16 and 30?

There are three commonly used methods to find the GCF of 16 and 30.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 16 and 30 by Prime Factorization?

To find the GCF of 16 and 30, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 30 = 2 × 3 × 5.
⇒ Since 2 is the only common prime factor of 16 and 30. Hence, GCF (16, 30) = 2.
☛ What are Prime Numbers?

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