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HCF of 48 and 54

HCF of 48 and 54 is the largest possible number that divides 48 and 54 exactly without any remainder. The factors of 48 and 54 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There are 3 commonly used methods to find the HCF of 48 and 54 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 48 and 54
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 48 and 54?

Answer: HCF of 48 and 54 is 6.

Explanation:

The HCF of two non-zero integers, x(48) and y(54), is the highest positive integer m(6) that divides both x(48) and y(54) without any remainder.

Methods to Find HCF of 48 and 54

Let's look at the different methods for finding the HCF of 48 and 54.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 48 and 54 by Long Division

HCF of 48 and 54 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 54 (larger number) by 48 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (48) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 48 and 54.

HCF of 48 and 54 by Listing Common Factors

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

There are 4 common factors of 48 and 54, that are 1, 2, 3, and 6. Therefore, the highest common factor of 48 and 54 is 6.

HCF of 48 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 = 54 and Y = 48

HCF(54, 48) = HCF(48, 54 mod 48) = HCF(48, 6)
HCF(48, 6) = HCF(6, 48 mod 6) = HCF(6, 0)
HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 48 and 54 is 6.

☛ Also Check:

HCF of 48 and 54 Examples

Example 1: Find the HCF of 48 and 54, if their LCM is 432.

Solution:

∵ LCM × HCF = 48 × 54
⇒ HCF(48, 54) = (48 × 54)/432 = 6
Therefore, the highest common factor of 48 and 54 is 6.
Example 2: The product of two numbers is 2592. If their HCF is 6, what is their LCM?

Solution:

Given: HCF = 6 and product of numbers = 2592
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 2592/6
Therefore, the LCM is 432.
Example 3: For two numbers, HCF = 6 and LCM = 432. If one number is 54, find the other number.

Solution:

Given: HCF (y, 54) = 6 and LCM (y, 54) = 432
∵ HCF × LCM = 54 × (y)
⇒ y = (HCF × LCM)/54
⇒ y = (6 × 432)/54
⇒ y = 48
Therefore, the other number is 48.

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FAQs on HCF of 48 and 54

What is the HCF of 48 and 54?

The HCF of 48 and 54 is 6. To calculate the Highest common factor of 48 and 54, we need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the highest factor that exactly divides both 48 and 54, i.e., 6.

How to Find the HCF of 48 and 54 by Prime Factorization?

To find the HCF of 48 and 54, we will find the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × 2 × 3; 54 = 2 × 3 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 48 and 54. Hence, HCF(48, 54) = 2 × 3 = 6
☛ Prime Numbers

What is the Relation Between LCM and HCF of 48, 54?

The following equation can be used to express the relation between LCM and HCF of 48 and 54, i.e. HCF × LCM = 48 × 54.

How to Find the HCF of 48 and 54 by Long Division Method?

To find the HCF of 48, 54 using long division method, 54 is divided by 48. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 48 and 54?

There are three commonly used methods to find the HCF of 48 and 54.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the HCF of 54 and 48 is 6, Find its LCM.

HCF(54, 48) × LCM(54, 48) = 54 × 48
Since the HCF of 54 and 48 = 6
⇒ 6 × LCM(54, 48) = 2592
Therefore, LCM = 432
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