How to Find GCF of 38/328, 83/178, 494/656?

GCF of 38/328, 83/178, 494/656

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 38/328, 83/178, 494/656 i.e 1/58384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 38/328, 83/178, 494/656.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 38/328,83/178,494/656?

Given fractions are 38/328,83/178,494/656

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 38/328,83/178,494/656, numerators are 38,83,494

Denominators are 328,178,656

The GCF of 38,83,494 is 1 .

LCM of 328,178,656 is 58384.

The greatest common factor of 38/328,83/178,494/656 = [GCF of 38,83,494]/[LCM of 328,178,656]= 1/58384

Therefore, the GCF of 38/328,83/178,494/656 is 1/58384.

Greatest Common Factor of 38,83,494

To find the highest common factor of 38,83,494, we have to find the factors of both numbers and list the highest common factor.

The factors of 38 are 1, 2, 19, 38

The factors of 83 are 1, 83

The factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494

The HCF of 38,83,494 is 1.

Lets's calculate GCF of 38,83,494

Greatest Common Factor (GCF) of 38,83,494 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 38,83,494 By Matching Biggest Common Factor Method

Now, list down the factors of 38

1,2,19,38

Now, list down the factors of 83

1,83

Now, list down the factors of 494

1,2,13,19,26,38,247,494

Greatest Common Factor

We found the factors 38,83,494 . The biggest common factor number is the GCF number.
So the greatest common factor 38,83,494 is 1.

Lets's calculate LCM of 328,178,656

Lowest Common Multiple of 328,178,656 using Common Division

2	328, 178, 656
2	164, 89, 328
2	82, 89, 164
41	41, 89, 82
	1, 89, 2

∴ So the LCM of the given numbers is 2 x 2 x 2 x 41 x 1 x 89 x 2 = 58384

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/58384

Therefore, the GCF of Fractions 38/328,83/178,494/656 is 1/58384

Least Common Multiple of 328,178,656 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 328,178,656 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(328,178,656) = 2

common factors(in case of two or more numbers have common factors) = 328

GCF(328,178,656) x common factors =2 x 328 = 656

LCM(328,178,656) = ( 328 × 178 × 656 ) / 656

LCM(328,178,656) = 38299904 / 656

LCM(328,178,656) = 58384

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 38/328, 83/178, 494/656

1. What is the HCF of 38,83,494?

The HCF of 38,83,494 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 38/328, 83/178, 494/656?

Answer: GCF of Numerators as per given numbers 38/328, 83/178, 494/656 is

GCF of Numerators i.e. for 38,83,494 is 1

LCM of denominators i.e. for 328,178,656 is 58384.

Thus, GCF of Fractions is 1/58384.Finally, GCF of Fractions for 38/328, 83/178, 494/656 is 1/58384.