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GCF of 12 and 64

GCF of 12 and 64 is the largest possible number that divides 12 and 64 exactly without any remainder. The factors of 12 and 64 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 8, 16, 32, 64 respectively. There are 3 commonly used methods to find the GCF of 12 and 64 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 12 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 64?

Answer: GCF of 12 and 64 is 4.

Explanation:

The GCF of two non-zero integers, x(12) and y(64), is the greatest positive integer m(4) that divides both x(12) and y(64) without any remainder.

Methods to Find GCF of 12 and 64

Let's look at the different methods for finding the GCF of 12 and 64.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 12 and 64 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 = 64 and Y = 12

GCF(64, 12) = GCF(12, 64 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 12 and 64 is 4.

GCF of 12 and 64 by Long Division

GCF of 12 and 64 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 64 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 12 and 64.

GCF of 12 and 64 by Prime Factorization

Prime factorization of 12 and 64 is (2 × 2 × 3) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 12 and 64 have common prime factors. Hence, the GCF of 12 and 64 is 2 × 2 = 4.

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GCF of 12 and 64 Examples

Example 1: Find the greatest number that divides 12 and 64 exactly.

Solution:

The greatest number that divides 12 and 64 exactly is their greatest common factor, i.e. GCF of 12 and 64.
⇒ Factors of 12 and 64:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
Therefore, the GCF of 12 and 64 is 4.
Example 2: The product of two numbers is 768. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 768
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 768/4
Therefore, the LCM is 192.
Example 3: Find the GCF of 12 and 64, if their LCM is 192.

Solution:

∵ LCM × GCF = 12 × 64
⇒ GCF(12, 64) = (12 × 64)/192 = 4
Therefore, the greatest common factor of 12 and 64 is 4.

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FAQs on GCF of 12 and 64

What is the GCF of 12 and 64?

The GCF of 12 and 64 is 4. To calculate the GCF (Greatest Common Factor) of 12 and 64, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides both 12 and 64, i.e., 4.

If the GCF of 64 and 12 is 4, Find its LCM.

GCF(64, 12) × LCM(64, 12) = 64 × 12
Since the GCF of 64 and 12 = 4
⇒ 4 × LCM(64, 12) = 768
Therefore, LCM = 192
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 12, 64?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 12 and 64, i.e. GCF × LCM = 12 × 64.

What are the Methods to Find GCF of 12 and 64?

There are three commonly used methods to find the GCF of 12 and 64.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 12 and 64 by Long Division Method?

To find the GCF of 12, 64 using long division method, 64 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 64 by Prime Factorization?

To find the GCF of 12 and 64, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 64. Hence, GCF(12, 64) = 2 × 2 = 4
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