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GCF of 16, 27 and 20

GCF of 16, 27 and 20 is the largest possible number that divides 16, 27 and 20 exactly without any remainder. The factors of 16, 27 and 20 are (1, 2, 4, 8, 16), (1, 3, 9, 27) and (1, 2, 4, 5, 10, 20) respectively. There are 3 commonly used methods to find the GCF of 16, 27 and 20 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 16, 27 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16, 27 and 20?

Answer: GCF of 16, 27 and 20 is 1.

Explanation:

The GCF of three non-zero integers, x(16), y(27) and z(20), is the greatest positive integer m(1) that divides x(16), y(27) and z(20) without any remainder.

Methods to Find GCF of 16, 27 and 20

The methods to find the GCF of 16, 27 and 20 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 16, 27 and 20 by Prime Factorization

Prime factorization of 16, 27 and 20 is (2 × 2 × 2 × 2), (3 × 3 × 3) and (2 × 2 × 5) respectively. As visible, there are no common prime factors between 16, 27 and 20, i.e. they are co-prime. Hence, the GCF of 16, 27 and 20 will be 1.

GCF of 16, 27 and 20 by Long Division

GCF of 16, 27 and 20 can be represented as GCF of (GCF of 16, 27) and 20. GCF(16, 27, 20) can be thus calculated by first finding GCF(16, 27) using long division and thereafter using this result with 20 to perform long division again.

Step 1: Divide 27 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (11). Repeat this process until the remainder = 0.
⇒ GCF(16, 27) = 1.
Step 3: Now to find the GCF of 1 and 20, we will perform a long division on 20 and 1.
Step 4: For remainder = 0, divisor = 1 ⇒ GCF(1, 20) = 1

Thus, GCF(16, 27, 20) = GCF(GCF(16, 27), 20) = 1.

GCF of 16, 27 and 20 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 27: 1, 3, 9, 27
Factors of 20: 1, 2, 4, 5, 10, 20

Since, 1 is the only common factor between 16, 27 and 20. The Greatest Common Factor of 16, 27 and 20 is 1.

☛ Also Check:

GCF of 16, 27 and 20 Examples

Example 1: Verify the relation between the LCM and GCF of 16, 27 and 20.

Solution:

The relation between the LCM and GCF of 16, 27 and 20 is given as, GCF(16, 27, 20) = [(16 × 27 × 20) × LCM(16, 27, 20)]/[LCM(16, 27) × LCM (27, 20) × LCM(16, 20)]
⇒ Prime factorization of 16, 27 and 20:
- 16 = 2 × 2 × 2 × 2
- 27 = 3 × 3 × 3
- 20 = 2 × 2 × 5
∴ LCM of (16, 27), (27, 20), (16, 20), and (16, 27, 20) is 432, 540, 80, and 2160 respectively.
Now, LHS = GCF(16, 27, 20) = 1.
And, RHS = [(16 × 27 × 20) × LCM(16, 27, 20)]/[LCM(16, 27) × LCM (27, 20) × LCM(16, 20)] = [(8640) × 2160]/[432 × 540 × 80]
LHS = RHS = 1.
Hence verified.
Example 2: Calculate the GCF of 16, 27, and 20 using LCM of the given numbers.

Solution:

Prime factorization of 16, 27 and 20 is given as,
- 16 = 2 × 2 × 2 × 2
- 27 = 3 × 3 × 3
- 20 = 2 × 2 × 5
LCM(16, 27) = 432, LCM(27, 20) = 540, LCM(20, 16) = 80, LCM(16, 27, 20) = 2160
⇒ GCF(16, 27, 20) = [(16 × 27 × 20) × LCM(16, 27, 20)]/[LCM(16, 27) × LCM (27, 20) × LCM(20, 16)]
⇒ GCF(16, 27, 20) = (8640 × 2160)/(432 × 540 × 80)
⇒ GCF(16, 27, 20) = 1.
Therefore, the GCF of 16, 27 and 20 is 1.
Example 3: Find the greatest number that divides 16, 27, and 20 completely.

Solution:

The greatest number that divides 16, 27, and 20 exactly is their greatest common factor.
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 27 = 1, 3, 9, 27
- Factors of 20 = 1, 2, 4, 5, 10, 20
The GCF of 16, 27, and 20 is 1.
∴ The greatest number that divides 16, 27, and 20 is 1.

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FAQs on GCF of 16, 27 and 20

What is the GCF of 16, 27 and 20?

The GCF of 16, 27 and 20 is 1. To calculate the GCF of 16, 27 and 20, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 27 = 1, 3, 9, 27; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides 16, 27 and 20, i.e., 1.

Which of the following is GCF of 16, 27 and 20? 1, 32, 61, 74, 72, 50

GCF of 16, 27, 20 will be the number that divides 16, 27, and 20 without leaving any remainder. The only number that satisfies the given condition is 1.

What are the Methods to Find GCF of 16, 27 and 20?

There are three commonly used methods to find the GCF of 16, 27 and 20.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 16, 27 and 20 by Prime Factorization?

To find the GCF of 16, 27 and 20, we will find the prime factorization of given numbers, i.e. 16 = 2 × 2 × 2 × 2; 27 = 3 × 3 × 3; 20 = 2 × 2 × 5.
⇒ There is no common prime factor for 16, 27 and 20. Hence, GCF(16, 27, 20) = 1.
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What is the Relation Between LCM and GCF of 16, 27 and 20?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 16, 27 and 20, i.e. GCF(16, 27, 20) = [(16 × 27 × 20) × LCM(16, 27, 20)]/[LCM(16, 27) × LCM (27, 20) × LCM(16, 20)].
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