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GCF of 32 and 60

GCF of 32 and 60 is the largest possible number that divides 32 and 60 exactly without any remainder. The factors of 32 and 60 are 1, 2, 4, 8, 16, 32 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 32 and 60 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 32 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 32 and 60?

Answer: GCF of 32 and 60 is 4.

Explanation:

The GCF of two non-zero integers, x(32) and y(60), is the greatest positive integer m(4) that divides both x(32) and y(60) without any remainder.

Methods to Find GCF of 32 and 60

Let's look at the different methods for finding the GCF of 32 and 60.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 32 and 60 by Long Division

GCF of 32 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 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (28).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 32 and 60.

GCF of 32 and 60 by Prime Factorization

Prime factorization of 32 and 60 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 3 × 5) respectively. As visible, 32 and 60 have common prime factors. Hence, the GCF of 32 and 60 is 2 × 2 = 4.

GCF of 32 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 = 32

GCF(60, 32) = GCF(32, 60 mod 32) = GCF(32, 28)
GCF(32, 28) = GCF(28, 32 mod 28) = GCF(28, 4)
GCF(28, 4) = GCF(4, 28 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 32 and 60 is 4.

☛ Also Check:

GCF of 32 and 60 Examples

Example 1: Find the greatest number that divides 32 and 60 exactly.

Solution:

The greatest number that divides 32 and 60 exactly is their greatest common factor, i.e. GCF of 32 and 60.
⇒ Factors of 32 and 60:
- Factors of 32 = 1, 2, 4, 8, 16, 32
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the GCF of 32 and 60 is 4.
Example 2: Find the GCF of 32 and 60, if their LCM is 480.

Solution:

∵ LCM × GCF = 32 × 60
⇒ GCF(32, 60) = (32 × 60)/480 = 4
Therefore, the greatest common factor of 32 and 60 is 4.
Example 3: For two numbers, GCF = 4 and LCM = 480. If one number is 32, find the other number.

Solution:

Given: GCF (x, 32) = 4 and LCM (x, 32) = 480
∵ GCF × LCM = 32 × (x)
⇒ x = (GCF × LCM)/32
⇒ x = (4 × 480)/32
⇒ x = 60
Therefore, the other number is 60.

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FAQs on GCF of 32 and 60

What is the GCF of 32 and 60?

The GCF of 32 and 60 is 4. To calculate the GCF of 32 and 60, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 32 and 60, i.e., 4.

How to Find the GCF of 32 and 60 by Long Division Method?

To find the GCF of 32, 60 using long division method, 60 is divided by 32. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 32 and 60 by Prime Factorization?

To find the GCF of 32 and 60, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 32 and 60. Hence, GCF(32, 60) = 2 × 2 = 4
☛ Prime Numbers

What is the Relation Between LCM and GCF of 32, 60?

The following equation can be used to express the relation between Least Common Multiple and GCF of 32 and 60, i.e. GCF × LCM = 32 × 60.

If the GCF of 60 and 32 is 4, Find its LCM.

GCF(60, 32) × LCM(60, 32) = 60 × 32
Since the GCF of 60 and 32 = 4
⇒ 4 × LCM(60, 32) = 1920
Therefore, LCM = 480
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 32 and 60?

There are three commonly used methods to find the GCF of 32 and 60.

By Prime Factorization
By Euclidean Algorithm
By Long Division

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