Factors Of 48 And 54

GCF of 48 and 54

GCF 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, six, eight, 12, 16, 24, 48 and 1, ii, 3, 6, nine, xviii, 27, 54 respectively. There are three commonly used methods to discover the GCF of 48 and 54 - long division, Euclidean algorithm, and prime factorization.

ane.	GCF of 48 and 54
2.	Listing of Methods
three.	Solved Examples
four.	FAQs

What is GCF of 48 and 54?

Answer: GCF of 48 and 54 is half dozen.

GCF of 48 and 54

Explanation:

The GCF of two not-zippo integers, 10(48) and y(54), is the greatest positive integer 1000(half dozen) that divides both 10(48) and y(54) without any rest.

Methods to Notice GCF of 48 and 54

The methods to find the GCF of 48 and 54 are explained below.

Listing Common Factors
Long Partition Method
Using Euclid's Algorithm

GCF of 48 and 54 by Listing Common Factors

Factors of 48: one, 2, 3, four, half-dozen, 8, 12, 16, 24, 48
Factors of 54: i, 2, 3, 6, 9, 18, 27, 54

There are 4 common factors of 48 and 54, that are one, 2, 3, and six. Therefore, the greatest common factor of 48 and 54 is six.

GCF of 48 and 54 past Long Division

GCF of 48 and 54 by Long Division

GCF of 48 and 54 is the divisor that we get when the rest becomes 0 afterwards doing long division repeatedly.

Step ane: Split 54 (larger number) by 48 (smaller number).
Step ii: Since the residual ≠ 0, we volition separate the divisor of step 1 (48) past the rest (6).
Step 3: Repeat this process until the residue = 0.

The respective divisor (6) is the GCF of 48 and 54.

GCF of 48 and 54 past Euclidean Algorithm

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

Here X = 54 and Y = 48

GCF(54, 48) = GCF(48, 54 modern 48) = GCF(48, 6)
GCF(48, vi) = GCF(6, 48 mod half-dozen) = GCF(6, 0)
GCF(half dozen, 0) = 6 (∵ GCF(X, 0) = |10|, where X ≠ 0)

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

☛ Besides Check:

GCF of 48 and 72 = 24
GCF of 45 and 63 = 9
GCF of 12 and nine = 3
GCF of lxxx and 20 = twenty
GCF of 35, 56 and 63 = 7
GCF of 14 and 24 = two
GCF of five and 10 = 5

GCF of 48 and 54 Examples

Case 1: The product of two numbers is 2592. If their GCF is vi, what is their LCM?

Solution:

Given: GCF = six and product of numbers = 2592
∵ LCM × GCF = production of numbers
⇒ LCM = Production/GCF = 2592/6
Therefore, the LCM is 432.
Case two: For two numbers, GCF = 6 and LCM = 432. If 1 number is 48, find the other number.

Solution:

Given: GCF (x, 48) = 6 and LCM (10, 48) = 432
∵ GCF × LCM = 48 × (x)
⇒ x = (GCF × LCM)/48
⇒ 10 = (6 × 432)/48
⇒ 10 = 54
Therefore, the other number is 54.
Example 3: Detect the greatest number that divides 48 and 54 exactly.

Solution:

The greatest number that divides 48 and 54 exactly is their greatest common factor, i.due east. GCF of 48 and 54.
⇒ Factors of 48 and 54:
- Factors of 48 = one, 2, 3, iv, vi, eight, 12, 16, 24, 48
- Factors of 54 = 1, two, iii, 6, 9, 18, 27, 54
Therefore, the GCF of 48 and 54 is half-dozen.

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FAQs on GCF of 48 and 54

What is the GCF of 48 and 54?

The GCF of 48 and 54 is 6 . To calculate the greatest common factor (GCF) of 48 and 54, nosotros need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 54 = 1, ii, three, 6, ix, 18, 27, 54) and choose the greatest factor that exactly divides both 48 and 54, i.e., 6.

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

There are 3 normally used methods to observe the GCF of 48 and 54.

By Euclidean Algorithm
Past Long Division
By Prime number Factorization

If the GCF of 54 and 48 is six, Observe its LCM.

GCF(54, 48) × LCM(54, 48) = 54 × 48
Since the GCF of 54 and 48 = half dozen
⇒ 6 × LCM(54, 48) = 2592
Therefore, LCM = 432
☛ GCF Estimator

How to Detect the GCF of 48 and 54 by Long Division Method?

To detect the GCF of 48, 54 using long partition method, 54 is divided by 48. The corresponding divisor (6) when remainder equals 0 is taken every bit GCF.

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

The following equation can be used to limited the relation betwixt LCM and GCF of 48 and 54, i.east. GCF × LCM = 48 × 54.

How to Discover the GCF of 48 and 54 by Prime Factorization?

To find the GCF of 48 and 54, we will detect the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × two × iii; 54 = 2 × 3 × three × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 48 and 54. Hence, GCF(48, 54) = two × iii = 6
☛ What is a Prime Number?