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GCF of 44, 12 and 28

GCF of 44, 12 and 28 is the largest possible number that divides 44, 12 and 28 exactly without any remainder. The factors of 44, 12 and 28 are (1, 2, 4, 11, 22, 44), (1, 2, 3, 4, 6, 12) and (1, 2, 4, 7, 14, 28) respectively. There are 3 commonly used methods to find the GCF of 44, 12 and 28 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 44, 12 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 44, 12 and 28?

Answer: GCF of 44, 12 and 28 is 4.

Explanation:

The GCF of three non-zero integers, x(44), y(12) and z(28), is the greatest positive integer m(4) that divides x(44), y(12) and z(28) without any remainder.

Methods to Find GCF of 44, 12 and 28

Let's look at the different methods for finding the GCF of 44, 12 and 28.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 44, 12 and 28 by Long Division

GCF of 44, 12 and 28 can be represented as GCF of (GCF of 44, 12) and 28. GCF(44, 12, 28) can be thus calculated by first finding GCF(44, 12) using long division and thereafter using this result with 28 to perform long division again.

Step 1: Divide 44 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (8). Repeat this process until the remainder = 0.
⇒ GCF(44, 12) = 4.
Step 3: Now to find the GCF of 4 and 28, we will perform a long division on 28 and 4.
Step 4: For remainder = 0, divisor = 4 ⇒ GCF(4, 28) = 4

Thus, GCF(44, 12, 28) = GCF(GCF(44, 12), 28) = 4.

GCF of 44, 12 and 28 by Prime Factorization

Prime factorization of 44, 12 and 28 is (2 × 2 × 11), (2 × 2 × 3) and (2 × 2 × 7) respectively. As visible, 44, 12 and 28 have common prime factors. Hence, the GCF of 44, 12 and 28 is 2 × 2 = 4.

GCF of 44, 12 and 28 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(44, 12, 28) = GCF(GCF(44, 12), 28)

GCF(44, 12) = GCF(12, 44 mod 12) = GCF(12, 8)
GCF(12, 8) = GCF(8, 12 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, 28)

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 44, 12 and 28 is 4.

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GCF of 44, 12 and 28 Examples

Example 1: Verify the relation between the LCM and GCF of 44, 12 and 28.

Solution:

The relation between the LCM and GCF of 44, 12 and 28 is given as, GCF(44, 12, 28) = [(44 × 12 × 28) × LCM(44, 12, 28)]/[LCM(44, 12) × LCM (12, 28) × LCM(44, 28)]
⇒ Prime factorization of 44, 12 and 28:
- 44 = 2 × 2 × 11
- 12 = 2 × 2 × 3
- 28 = 2 × 2 × 7
∴ LCM of (44, 12), (12, 28), (44, 28), and (44, 12, 28) is 132, 84, 308, and 924 respectively.
Now, LHS = GCF(44, 12, 28) = 4.
And, RHS = [(44 × 12 × 28) × LCM(44, 12, 28)]/[LCM(44, 12) × LCM (12, 28) × LCM(44, 28)] = [(14784) × 924]/[132 × 84 × 308]
LHS = RHS = 4.
Hence verified.
Example 2: Calculate the GCF of 44, 12, and 28 using LCM of the given numbers.

Solution:

Prime factorization of 44, 12 and 28 is given as,
- 44 = 2 × 2 × 11
- 12 = 2 × 2 × 3
- 28 = 2 × 2 × 7
LCM(44, 12) = 132, LCM(12, 28) = 84, LCM(28, 44) = 308, LCM(44, 12, 28) = 924
⇒ GCF(44, 12, 28) = [(44 × 12 × 28) × LCM(44, 12, 28)]/[LCM(44, 12) × LCM (12, 28) × LCM(28, 44)]
⇒ GCF(44, 12, 28) = (14784 × 924)/(132 × 84 × 308)
⇒ GCF(44, 12, 28) = 4.
Therefore, the GCF of 44, 12 and 28 is 4.
Example 3: Find the greatest number that divides 44, 12, and 28 completely.

Solution:

The greatest number that divides 44, 12, and 28 exactly is their greatest common factor.
- Factors of 44 = 1, 2, 4, 11, 22, 44
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 28 = 1, 2, 4, 7, 14, 28
The GCF of 44, 12, and 28 is 4.
∴ The greatest number that divides 44, 12, and 28 is 4.

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FAQs on GCF of 44, 12 and 28

What is the GCF of 44, 12 and 28?

The GCF of 44, 12 and 28 is 4. To calculate the greatest common factor (GCF) of 44, 12 and 28, we need to factor each number (factors of 44 = 1, 2, 4, 11, 22, 44; factors of 12 = 1, 2, 3, 4, 6, 12; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides 44, 12 and 28, i.e., 4.

What are the Methods to Find GCF of 44, 12 and 28?

There are three commonly used methods to find the GCF of 44, 12 and 28.

By Listing Common Factors
By Long Division
By Prime Factorization

Which of the following is GCF of 44, 12 and 28? 4, 72, 82, 86, 72, 91, 63

GCF of 44, 12, 28 will be the number that divides 44, 12, and 28 without leaving any remainder. The only number that satisfies the given condition is 4.

How to Find the GCF of 44, 12 and 28 by Prime Factorization?

To find the GCF of 44, 12 and 28, we will find the prime factorization of given numbers, i.e. 44 = 2 × 2 × 11; 12 = 2 × 2 × 3; 28 = 2 × 2 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 44, 12 and 28. Hence, GCF(44, 12, 28) = 2 × 2 = 4
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 44, 12 and 28?

The following equation can be used to express the relation between LCM and GCF of 44, 12 and 28, i.e. GCF(44, 12, 28) = [(44 × 12 × 28) × LCM(44, 12, 28)]/[LCM(44, 12) × LCM (12, 28) × LCM(44, 28)].
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