The HCF of 336 and 54 is 6. The highest possible number that divides 336 and 54 perfectly without any residue is the HCF of 336 and 54. The factors of 336 and 54 are (1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336) and (1, 2, 3, 6, 9, 18, 27, 54), respectively. Prime factorisation, listing common factors, and long division are the three common methods for calculating the HCF of 336 and 54.
Also read: Highest common factor
What is the HCF of 336 and 54?
The answer to this question is 6. This article shows how to find the HCF of 336 and 54 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 336 and 54?
There are three methods to find the HCF of 336 and 54:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 336 and 54 by Prime Factorisation Method
The prime factorisation of 336 and 54 is given by:
Prime factorisation of 336 = (2 × 2 × 2 × 2 × 3 × 7)
Prime factorisation of 54 = (2 × 3 × 3 × 3)
Since the common prime factors of 336 and 54 are 2 and 3, the HCF of 336 and 54 is 2 × 3 = 6.
Hence, HCF (336, 54) = 6
HCF of 336 and 54 by Long Division Method
The divisor that we receive when the remainder becomes 0 after executing a long division repeatedly is HCF of 336 and 54.
No further division can be done.
Hence, HCF (336, 54) = 6
HCF of 336 and 54 by Listing Common Factors
To calculate the HCF of 336 and 54 by listing out the common factors, list the factors as shown below:
Factors of 336: 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
There are 4 common factors of 336 and 54, and they are 1, 2, 3, and 6.
Therefore, the highest common factor of 336 and 54 is 6.
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HCF of 336 and 54 Solved Example
Question: For two numbers, HCF = 6 and LCM = 3024. If one number is 54, find the other number.
Solution:
Given: HCF (y, 54) = 6 and LCM (y, 54) = 3024
∵ HCF × LCM = 54 × (y)
⇒ y = (HCF × LCM)/54
⇒ y = (6 × 3024)/54
⇒ y = 18144/54 = 336
Therefore, the other number is 336.
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