HCF of 336 and 54

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.

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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Video Lesson on Properties of HCF and LCM

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.

Frequently Asked Questions on HCF of 336 and 54

Q1

What is the HCF of 336 and 54?

The HCF of 336 and 54 is 6. To find the largest factor that divides both 336 and 54 exactly, i.e. 6, we must factor each number (factors of 336 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336 and factors of 54 = 1, 2, 3, 6, 9, 18, 27).
Q2

How to find the HCF of 336 and 54 by long division method?

To find the HCF of 336 and 54 using the long division method, 336 is divided by 54. The corresponding divisor (6) when remainder equals 0 is taken as HCF.
Q3

What are the methods to find HCF of 336 and 54?

There are three commonly used methods to find the HCF of 336 and 54, and they are: Long Division Method Listing Common Factors Prime Factorisation

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