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GCF of 64 and 120

GCF of 64 and 120 is the largest possible number that divides 64 and 120 exactly without any remainder. The factors of 64 and 120 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the GCF of 64 and 120 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 64 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 64 and 120?

Answer: GCF of 64 and 120 is 8.

Explanation:

The GCF of two non-zero integers, x(64) and y(120), is the greatest positive integer m(8) that divides both x(64) and y(120) without any remainder.

Methods to Find GCF of 64 and 120

Let's look at the different methods for finding the GCF of 64 and 120.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 64 and 120 by Prime Factorization

Prime factorization of 64 and 120 is (2 × 2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 3 × 5) respectively. As visible, 64 and 120 have common prime factors. Hence, the GCF of 64 and 120 is 2 × 2 × 2 = 8.

GCF of 64 and 120 by Long Division

GCF of 64 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 64 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (64) by the remainder (56).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (8) is the GCF of 64 and 120.

GCF of 64 and 120 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 = 120 and Y = 64

GCF(120, 64) = GCF(64, 120 mod 64) = GCF(64, 56)
GCF(64, 56) = GCF(56, 64 mod 56) = GCF(56, 8)
GCF(56, 8) = GCF(8, 56 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 64 and 120 is 8.

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GCF of 64 and 120 Examples

Example 1: The product of two numbers is 7680. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 7680
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 7680/8
Therefore, the LCM is 960.
Example 2: Find the GCF of 64 and 120, if their LCM is 960.

Solution:

∵ LCM × GCF = 64 × 120
⇒ GCF(64, 120) = (64 × 120)/960 = 8
Therefore, the greatest common factor of 64 and 120 is 8.
Example 3: Find the greatest number that divides 64 and 120 exactly.

Solution:

The greatest number that divides 64 and 120 exactly is their greatest common factor, i.e. GCF of 64 and 120.
⇒ Factors of 64 and 120:
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the GCF of 64 and 120 is 8.

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FAQs on GCF of 64 and 120

What is the GCF of 64 and 120?

The GCF of 64 and 120 is 8. To calculate the greatest common factor (GCF) of 64 and 120, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the greatest factor that exactly divides both 64 and 120, i.e., 8.

How to Find the GCF of 64 and 120 by Prime Factorization?

To find the GCF of 64 and 120, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 64 and 120. Hence, GCF(64, 120) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 64, 120?

The following equation can be used to express the relation between Least Common Multiple and GCF of 64 and 120, i.e. GCF × LCM = 64 × 120.

If the GCF of 120 and 64 is 8, Find its LCM.

GCF(120, 64) × LCM(120, 64) = 120 × 64
Since the GCF of 120 and 64 = 8
⇒ 8 × LCM(120, 64) = 7680
Therefore, LCM = 960
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How to Find the GCF of 64 and 120 by Long Division Method?

To find the GCF of 64, 120 using long division method, 120 is divided by 64. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 64 and 120?

There are three commonly used methods to find the GCF of 64 and 120.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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