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HCF of 18, 54 and 81

HCF of 18, 54 and 81 is the largest possible number that divides 18, 54 and 81 exactly without any remainder. The factors of 18, 54 and 81 are (1, 2, 3, 6, 9, 18), (1, 2, 3, 6, 9, 18, 27, 54) and (1, 3, 9, 27, 81) respectively. There are 3 commonly used methods to find the HCF of 18, 54 and 81 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 18, 54 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18, 54 and 81?

Answer: HCF of 18, 54 and 81 is 9.

Explanation:

The HCF of three non-zero integers, x(18), y(54) and z(81), is the highest positive integer m(9) that divides x(18), y(54) and z(81) without any remainder.

Methods to Find HCF of 18, 54 and 81

The methods to find the HCF of 18, 54 and 81 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

HCF of 18, 54 and 81 by Prime Factorization

Prime factorization of 18, 54 and 81 is (2 × 3 × 3), (2 × 3 × 3 × 3) and (3 × 3 × 3 × 3) respectively. As visible, 18, 54 and 81 have common prime factors. Hence, the HCF of 18, 54 and 81 is 3 × 3 = 9.

HCF of 18, 54 and 81 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 81: 1, 3, 9, 27, 81

There are 3 common factors of 18, 54 and 81, that are 1, 3, and 9. Therefore, the highest common factor of 18, 54 and 81 is 9.

HCF of 18, 54 and 81 by Long Division

HCF of 18, 54 and 81 can be represented as HCF of (HCF of 18, 54) and 81. HCF(18, 54, 81) can be thus calculated by first finding HCF(18, 54) using long division and thereafter using this result with 81 to perform long division again.

Step 1: Divide 54 (larger number) by 18 (smaller number).
Step 2: Since the remainder = 0, the divisor (18) is the HCF(18, 54) = 18.
Step 3: Now to find the HCF of 18 and 81, we will perform a long division on 81 and 18.
Step 4: For remainder = 0, divisor = 9 ⇒ HCF(18, 81) = 9

Thus, HCF(18, 54, 81) = HCF(HCF(18, 54), 81) = 9.

☛ Also Check:

HCF of 18, 54 and 81 Examples

Example 1: Calculate the HCF of 18, 54, and 81 using LCM of the given numbers.

Solution:

Prime factorization of 18, 54 and 81 is given as,
- 18 = 2 × 3 × 3
- 54 = 2 × 3 × 3 × 3
- 81 = 3 × 3 × 3 × 3
LCM(18, 54) = 54, LCM(54, 81) = 162, LCM(81, 18) = 162, LCM(18, 54, 81) = 162
⇒ HCF(18, 54, 81) = [(18 × 54 × 81) × LCM(18, 54, 81)]/[LCM(18, 54) × LCM (54, 81) × LCM(81, 18)]
⇒ HCF(18, 54, 81) = (78732 × 162)/(54 × 162 × 162)
⇒ HCF(18, 54, 81) = 9.
Therefore, the HCF of 18, 54 and 81 is 9.
Example 2: Find the highest number that divides 18, 54, and 81 completely.

Solution:

The highest number that divides 18, 54, and 81 exactly is their highest common factor.
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 81 = 1, 3, 9, 27, 81
The HCF of 18, 54, and 81 is 9.
∴ The highest number that divides 18, 54, and 81 is 9.
Example 3: Verify the relation between the LCM and HCF of 18, 54 and 81.

Solution:

The relation between the LCM and HCF of 18, 54 and 81 is given as, HCF(18, 54, 81) = [(18 × 54 × 81) × LCM(18, 54, 81)]/[LCM(18, 54) × LCM (54, 81) × LCM(18, 81)]
⇒ Prime factorization of 18, 54 and 81:
- 18 = 2 × 3 × 3
- 54 = 2 × 3 × 3 × 3
- 81 = 3 × 3 × 3 × 3
∴ LCM of (18, 54), (54, 81), (18, 81), and (18, 54, 81) is 54, 162, 162, and 162 respectively.
Now, LHS = HCF(18, 54, 81) = 9.
And, RHS = [(18 × 54 × 81) × LCM(18, 54, 81)]/[LCM(18, 54) × LCM (54, 81) × LCM(18, 81)] = [(78732) × 162]/[54 × 162 × 162]
LHS = RHS = 9.
Hence verified.

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FAQs on HCF of 18, 54 and 81

What is the HCF of 18, 54 and 81?

The HCF of 18, 54 and 81 is 9. To calculate the highest common factor of 18, 54 and 81, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54; factors of 81 = 1, 3, 9, 27, 81) and choose the highest factor that exactly divides 18, 54 and 81, i.e., 9.

How to Find the HCF of 18, 54 and 81 by Prime Factorization?

To find the HCF of 18, 54 and 81, we will find the prime factorization of given numbers, i.e. 18 = 2 × 3 × 3; 54 = 2 × 3 × 3 × 3; 81 = 3 × 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 18, 54 and 81. Hence, HCF(18, 54, 81) = 3 × 3 = 9
☛ What is a Prime Number?

Which of the following is HCF of 18, 54 and 81? 9, 102, 96, 87, 87, 108, 114, 113, 99

HCF of 18, 54, 81 will be the number that divides 18, 54, and 81 without leaving any remainder. The only number that satisfies the given condition is 9.

What are the Methods to Find HCF of 18, 54 and 81?

There are three commonly used methods to find the HCF of 18, 54 and 81.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and HCF of 18, 54 and 81?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF of 18, 54 and 81, i.e. HCF(18, 54, 81) = [(18 × 54 × 81) × LCM(18, 54, 81)]/[LCM(18, 54) × LCM (54, 81) × LCM(18, 81)].
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