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GCF of 28, 48 and 64

GCF of 28, 48 and 64 is the largest possible number that divides 28, 48 and 64 exactly without any remainder. The factors of 28, 48 and 64 are (1, 2, 4, 7, 14, 28), (1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and (1, 2, 4, 8, 16, 32, 64) respectively. There are 3 commonly used methods to find the GCF of 28, 48 and 64 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 28, 48 and 64
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28, 48 and 64?

Answer: GCF of 28, 48 and 64 is 4.

Explanation:

The GCF of three non-zero integers, x(28), y(48) and z(64), is the greatest positive integer m(4) that divides x(28), y(48) and z(64) without any remainder.

Methods to Find GCF of 28, 48 and 64

The methods to find the GCF of 28, 48 and 64 are explained below.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 28, 48 and 64 by Prime Factorization

Prime factorization of 28, 48 and 64 is (2 × 2 × 7), (2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 2 × 2 × 2) respectively. As visible, 28, 48 and 64 have common prime factors. Hence, the GCF of 28, 48 and 64 is 2 × 2 = 4.

GCF of 28, 48 and 64 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 64: 1, 2, 4, 8, 16, 32, 64

There are 3 common factors of 28, 48 and 64, that are 1, 2, and 4. Therefore, the greatest common factor of 28, 48 and 64 is 4.

GCF of 28, 48 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.

GCF(28, 48, 64) = GCF(GCF(28, 48), 64)

GCF(48, 28) = GCF(28, 48 mod 28) = GCF(28, 20)
GCF(28, 20) = GCF(20, 28 mod 20) = GCF(20, 8)
GCF(20, 8) = GCF(8, 20 mod 8) = GCF(8, 4)
GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Steps for GCF(4, 64)

GCF(64, 4) = GCF(4, 64 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 28, 48 and 64 is 4.

☛ Also Check:

GCF of 28, 48 and 64 Examples

Example 1: Find the greatest number that divides 28, 48, and 64 completely.

Solution:

The greatest number that divides 28, 48, and 64 exactly is their greatest common factor.
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
The GCF of 28, 48, and 64 is 4.
∴ The greatest number that divides 28, 48, and 64 is 4.
Example 2: Calculate the GCF of 28, 48, and 64 using LCM of the given numbers.

Solution:

Prime factorization of 28, 48 and 64 is given as,
- 28 = 2 × 2 × 7
- 48 = 2 × 2 × 2 × 2 × 3
- 64 = 2 × 2 × 2 × 2 × 2 × 2
LCM(28, 48) = 336, LCM(48, 64) = 192, LCM(64, 28) = 448, LCM(28, 48, 64) = 1344
⇒ GCF(28, 48, 64) = [(28 × 48 × 64) × LCM(28, 48, 64)]/[LCM(28, 48) × LCM (48, 64) × LCM(64, 28)]
⇒ GCF(28, 48, 64) = (86016 × 1344)/(336 × 192 × 448)
⇒ GCF(28, 48, 64) = 4.
Therefore, the GCF of 28, 48 and 64 is 4.
Example 3: Verify the relation between the LCM and GCF of 28, 48 and 64.

Solution:

The relation between the LCM and GCF of 28, 48 and 64 is given as, GCF(28, 48, 64) = [(28 × 48 × 64) × LCM(28, 48, 64)]/[LCM(28, 48) × LCM (48, 64) × LCM(28, 64)]
⇒ Prime factorization of 28, 48 and 64:
- 28 = 2 × 2 × 7
- 48 = 2 × 2 × 2 × 2 × 3
- 64 = 2 × 2 × 2 × 2 × 2 × 2
∴ LCM of (28, 48), (48, 64), (28, 64), and (28, 48, 64) is 336, 192, 448, and 1344 respectively.
Now, LHS = GCF(28, 48, 64) = 4.
And, RHS = [(28 × 48 × 64) × LCM(28, 48, 64)]/[LCM(28, 48) × LCM (48, 64) × LCM(28, 64)] = [(86016) × 1344]/[336 × 192 × 448]
LHS = RHS = 4.
Hence verified.

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FAQs on GCF of 28, 48 and 64

What is the GCF of 28, 48 and 64?

The GCF of 28, 48 and 64 is 4. To calculate the GCF of 28, 48 and 64, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 64 = 1, 2, 4, 8, 16, 32, 64) and choose the greatest factor that exactly divides 28, 48 and 64, i.e., 4.

How to Find the GCF of 28, 48 and 64 by Prime Factorization?

To find the GCF of 28, 48 and 64, we will find the prime factorization of given numbers, i.e. 28 = 2 × 2 × 7; 48 = 2 × 2 × 2 × 2 × 3; 64 = 2 × 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 28, 48 and 64. Hence, GCF(28, 48, 64) = 2 × 2 = 4
☛ Prime Numbers

Which of the following is GCF of 28, 48 and 64? 4, 64, 91, 92, 79

GCF of 28, 48, 64 will be the number that divides 28, 48, and 64 without leaving any remainder. The only number that satisfies the given condition is 4.

What are the Methods to Find GCF of 28, 48 and 64?

There are three commonly used methods to find the GCF of 28, 48 and 64.

By Listing Common Factors
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 28, 48 and 64?

The following equation can be used to express the relation between LCM and GCF of 28, 48 and 64, i.e. GCF(28, 48, 64) = [(28 × 48 × 64) × LCM(28, 48, 64)]/[LCM(28, 48) × LCM (48, 64) × LCM(28, 64)].
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