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HCF of 336 and 54

HCF of 336 and 54 is the largest possible number that divides 336 and 54 exactly without any remainder. 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. There are 3 commonly used methods to find the HCF of 336 and 54 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 336 and 54
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 336 and 54?

Answer: HCF of 336 and 54 is 6.

Explanation:

The HCF of two non-zero integers, x(336) and y(54), is the highest positive integer m(6) that divides both x(336) and y(54) without any remainder.

Methods to Find HCF of 336 and 54

The methods to find the HCF of 336 and 54 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Prime Factorization Method

HCF of 336 and 54 by Listing Common Factors

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, that are 1, 2, 3, and 6. Therefore, the highest common factor of 336 and 54 is 6.

HCF of 336 and 54 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 336 and Y = 54

HCF(336, 54) = HCF(54, 336 mod 54) = HCF(54, 12)
HCF(54, 12) = HCF(12, 54 mod 12) = HCF(12, 6)
HCF(12, 6) = HCF(6, 12 mod 6) = HCF(6, 0)
HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 336 and 54 is 6.

HCF of 336 and 54 by Prime Factorization

Prime factorization of 336 and 54 is (2 × 2 × 2 × 2 × 3 × 7) and (2 × 3 × 3 × 3) respectively. As visible, 336 and 54 have common prime factors. Hence, the HCF of 336 and 54 is 2 × 3 = 6.

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HCF of 336 and 54 Examples

Example 1: 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 = 336
Therefore, the other number is 336.
Example 2: The product of two numbers is 18144. If their HCF is 6, what is their LCM?

Solution:

Given: HCF = 6 and product of numbers = 18144
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 18144/6
Therefore, the LCM is 3024.
Example 3: Find the highest number that divides 336 and 54 exactly.

Solution:

The highest number that divides 336 and 54 exactly is their highest common factor, i.e. HCF of 336 and 54.
⇒ Factors of 336 and 54:
- 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
Therefore, the HCF of 336 and 54 is 6.

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FAQs on HCF of 336 and 54

What is the HCF of 336 and 54?

The HCF of 336 and 54 is 6. To calculate the HCF of 336 and 54, we need to 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; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the highest factor that exactly divides both 336 and 54, i.e., 6.

How to Find the HCF of 336 and 54 by Long Division Method?

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

If the HCF of 54 and 336 is 6, Find its LCM.

HCF(54, 336) × LCM(54, 336) = 54 × 336
Since the HCF of 54 and 336 = 6
⇒ 6 × LCM(54, 336) = 18144
Therefore, LCM = 3024
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How to Find the HCF of 336 and 54 by Prime Factorization?

To find the HCF of 336 and 54, we will find the prime factorization of the given numbers, i.e. 336 = 2 × 2 × 2 × 2 × 3 × 7; 54 = 2 × 3 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 336 and 54. Hence, HCF(336, 54) = 2 × 3 = 6
☛ Prime Numbers

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.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and HCF of 336, 54?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 336 and 54, i.e. HCF × LCM = 336 × 54.

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