HCF of 54 288 and 360

The HCF of 54, 288 and 360 is 18. The listing common factors, prime factorisation and long division are the three most frequent methods used for calculating the HCF of 54, 288 and 360. The greatest number that divides 54, 288, and 360 perfectly and without a remainder is known as the HCF of these numbers. The factors of 54, 288 and 360 are:

54→ 1, 2, 3, 6, 9, 18, 27, 54

288→ 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

360→ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 

Also read: Highest common factor

What is the HCF of 54, 288 and 360?

The answer to this question is 18. This article shows how to find the HCF of 54, 288 and 360 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 54, 288 and 360?

There are three methods to find the HCF of 54, 288 and 360:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 54, 288 and 360 by Prime Factorisation Method

The prime factorisation of 54, 288 and 360 is given by:

Prime factorisation of 54 = (2 × 3 × 3 × 3)

Prime factorisation of 288 = (2 × 2 × 2 × 2 × 2 × 3 × 3)

Prime factorisation of 360 = (2 × 2 × 2 × 3 × 3 × 5)

Hence, the HCF of 54, 288 and 360 is 2 × 3 × 3 = 18

HCF (54, 288, 360) = 18

HCF of 54, 288 and 360 by Long Division Method

The divisor that we get when the remainder is 0 after doing long division repeatedly is the HCF of 54, 288 and 360.

HCF of 54 288 and 360

No further division can be done. 

Hence, HCF (54, 288, 360) = 18

HCF of 54, 288 and 360 by Listing Common Factors

To calculate the HCF of 54, 288 and 360 by listing common factors, list the factors as shown below:

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

Factors of 288: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

Factors of 360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

There are 6 common factors of 54, 288 and 360, and they are 1, 2, 3, 6, 9, and 18. Therefore, the Highest Common Factor of 54, 288 and 360 is 18.

Related Articles

Video Lesson on Properties of HCF and LCM

HCF of 54, 288 and 360 Solved Example

Find the highest number that divides 54, 288, and 360 completely.

Solution:

The highest number that divides 54, 288, and 360 exactly is their Highest Common Factor.

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

Factors of 288 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288

Factors of 360 = 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The HCF of 54, 288, and 360 is 18.

The highest number that divides 54, 288, and 360 is 18.

Frequently Asked Questions on HCF of 54, 288 and 360

Q1

What is the HCF of 54, 288 and 360?

The HCF of 54, 288 and 360 is 18. To calculate the HCF of 54, 288 and 360, we need to factor each number and choose the highest factor that exactly divides 54, 288 and 360. Hence the HCF of 54, 288 and 360 is 18.
Q2

How to find the HCF of 54, 288 and 360 by prime factorisation?

To find the HCF of 54, 288 and 360, we need to find the prime factorisation of given numbers, .i.. 54 = 2 × 3 × 3 × 3; 288 = 2 × 2 × 2 × 2 × 2 × 3 × 3; 360 = 2 × 2 × 2 × 3 × 3 × 5. ⇒ 2, 3, 3 are common terms in the prime factorisation of 54, 288 and 360. Hence, HCF(54, 288, 360) = 2 × 3 × 3 = 18
Q3

What are the methods to find HCF of 54, 288 and 360?

There are three commonly used methods to find the HCF of 54, 288 and 360. They are: Long Division Listing Common Factors Prime Factorisation
Q4

Which of the following is the HCF of 54, 288 and 360? 18, 362, 388, 374, 395, 401, 399, 371, 371

HCF of 54, 288, 360 is the number that divides 54, 288, and 360 without leaving any remainder. The only number that satisfies the given condition is 18.
Q5

What is the relation between LCM and HCF of 54, 288 and 360?

The following equation can be used to express the relation between LCM (Least Common Multiple) and HCF(Highest Common Factor) of 54, 288 and 360, .i.e HCF(54, 288, 360) = [(54 × 288 × 360) × LCM(54, 288, 360)]/[LCM(54, 288) × LCM (288, 360) × LCM(54, 360)].

Comments

Leave a Comment

Your Mobile number and Email id will not be published.

*

*