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GCF of 16 and 60

GCF of 16 and 60 is the largest possible number that divides 16 and 60 exactly without any remainder. The factors of 16 and 60 are 1, 2, 4, 8, 16 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 commonly used methods to find the GCF of 16 and 60 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 16 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 60?

Answer: GCF of 16 and 60 is 4.

Explanation:

The GCF of two non-zero integers, x(16) and y(60), is the greatest positive integer m(4) that divides both x(16) and y(60) without any remainder.

Methods to Find GCF of 16 and 60

The methods to find the GCF of 16 and 60 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 16 and 60 by Long Division

GCF of 16 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 16 and 60.

GCF of 16 and 60 by Prime Factorization

Prime factorization of 16 and 60 is (2 × 2 × 2 × 2) and (2 × 2 × 3 × 5) respectively. As visible, 16 and 60 have common prime factors. Hence, the GCF of 16 and 60 is 2 × 2 = 4.

GCF of 16 and 60 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 = 60 and Y = 16

GCF(60, 16) = GCF(16, 60 mod 16) = GCF(16, 12)
GCF(16, 12) = GCF(12, 16 mod 12) = GCF(12, 4)
GCF(12, 4) = GCF(4, 12 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 60 is 4.

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GCF of 16 and 60 Examples

Example 1: The product of two numbers is 960. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 960
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 960/4
Therefore, the LCM is 240.
Example 2: For two numbers, GCF = 4 and LCM = 240. If one number is 60, find the other number.

Solution:

Given: GCF (x, 60) = 4 and LCM (x, 60) = 240
∵ GCF × LCM = 60 × (x)
⇒ x = (GCF × LCM)/60
⇒ x = (4 × 240)/60
⇒ x = 16
Therefore, the other number is 16.
Example 3: Find the GCF of 16 and 60, if their LCM is 240.

Solution:

∵ LCM × GCF = 16 × 60
⇒ GCF(16, 60) = (16 × 60)/240 = 4
Therefore, the greatest common factor of 16 and 60 is 4.

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FAQs on GCF of 16 and 60

What is the GCF of 16 and 60?

The GCF of 16 and 60 is 4. To calculate the GCF of 16 and 60, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 16 and 60, i.e., 4.

If the GCF of 60 and 16 is 4, Find its LCM.

GCF(60, 16) × LCM(60, 16) = 60 × 16
Since the GCF of 60 and 16 = 4
⇒ 4 × LCM(60, 16) = 960
Therefore, LCM = 240
☛ Greatest Common Factor Calculator

How to Find the GCF of 16 and 60 by Long Division Method?

To find the GCF of 16, 60 using long division method, 60 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 16, 60?

The following equation can be used to express the relation between Least Common Multiple and GCF of 16 and 60, i.e. GCF × LCM = 16 × 60.

How to Find the GCF of 16 and 60 by Prime Factorization?

To find the GCF of 16 and 60, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 60. Hence, GCF(16, 60) = 2 × 2 = 4
☛ What are Prime Numbers?

What are the Methods to Find GCF of 16 and 60?

There are three commonly used methods to find the GCF of 16 and 60.

By Long Division
By Listing Common Factors
By Prime Factorization

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