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.
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.
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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.
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