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HCF

HCF of 336 and 54

Written by Prerit Jain

Updated on: 15 Feb 2023

HCF of 336 and 54

HCF of 336 and 54

HCF of 336 and 54: The HCF of any given number is the highest factor common for all the given numbers. They are the common highest factor numbers among the given numbers to solve. The number can be small or complex. The HCF is abbreviated as Highest Common Factor or Greatest Common Divisor.

What Is the HCF of 336 and 54?

There are three methods to find the HCF of any given number:

  • Listing Factor Method
  • Prime Factorization Method
  • Division Method

HCF of 336 and 54 Using the Listing Factor Method

The listing factor method to find the HCF of a given number is done by cataloging the factors and finding the common elements. The steps follow:
Step 1: Find the factors of the given numbers and align them.
Step 2: The highest factor that was common in all the numbers is the HCF
Therefore the HCF of 336 and 54 using the listing method is as follows:
Step 1: Find the factors of the given number and align them
The factor of 336 = 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, and 336.
The factor of 54 = 1, 2, 3, 6, 9, 18, 27, 54.
Step 2: The highest factor that is common is the HCF of the given numbers.
The common highest factor = 1,`2,3 and 6
The highest common factor is 6.
Hence, HCF (336,54) = 6.

HCF Of 336 and 54 Using the Prime Factorization Method

The prime factorization method is one of the most frequently used methods to find the HCF. The numbers that are prime are only taken into account. The step follows,
Step 1: Find the prime factor of the given numbers.
Step 2: Multiply the common prime numbers, which is the HCF of the given number.
Therefore, the HCF of 336 and 54 using the prime factorization method.
Step 1:Find the prime factor of the given numbers
The prime factor of 336 = 2✕2✕2✕2✕3✕7
The prime factor of 54 = 2✕3✕3✕3
The highest common prime numbers = 2✕3
Step 2: Multiply the common prime numbers, which is the HCF of the given number
Multiply the numbers 2✕3
The HCF of the given numbers (336,54) = 6

HCF of 336 and 54 Using the Long Division Method

The long division method can break down the highest numbers into smaller parts giving the HCF of any larger numbers. The steps follow,
Step 1: Divide the largest number with the smallest number till the zero
Step 2: The last divisor is the HCF of the given number.
Therefore, the HCF of 336 and 54 using the prime factorization method.
Step 1: Divide the largest number with the smallest number till the zero
Step 2: The last divisor is the HCF of the given number.
The last divisor is 6
Hence HCF (336,54) = 6.

Solved Examples:

Example 1: What are the HCF and LCM of 336 and 54?
The HCF of (336,54) = 6
The LCM of (336,54) = 3024

Example 2: What is the HCF of 52and 28 using the prime factorization method?
The prime factor of 52 = 2✕2✕13
The prime factor of 28 = 2✕2✕7
The HCF of (52,28) = 4

Example 3: What is the HCF of 42 and 30?
The factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42
The factors of 30 = 1, 2, 3, 5, 6, 10, 15 and 30.
The HCF (42, 30) = 6.

Example 4: What is the HCF of 36, 62, and 46?
The HCF (36,42,46) = 2

Example 5: What is the HCF of 336 and 54 if their LCM is 3024?
The HCF (336, 54 ) = 6.

Frequently Asked Questions (FAQ)

Find the LCM and HCF of 336 and 54 and verify that HCF LCM product of the two number?
The LCM of 336 and 54 = 3024
The HCF of 336 and 54 = 6
The product of LCM and HCF = 3024✕6 = 18,144

Find the HCF of 336 and 54 by prime factorization.
The prime factor of 336 = 2✕2✕2✕2✕3✕7
The prime factor of 54 = 2✕3✕3✕3
Hence, HCF (336,54) = 6.

Find the LCM and HCF of 12, 15, and 21?
The LCM (12,15,21) = 420
The HCF (12,15,21) = 3

Find the HCF of 336 and 54 by division method?
HCF (336,54) = 6.

Find the HCF of 64 and 44?
The HCF (64,44) = 4.

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Prerit Jain

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