How to Find GCF of 83/76, 478/22, 190/208?

GCF of 83/76, 478/22, 190/208

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 83/76, 478/22, 190/208 i.e 1/43472 easily. The following is the detailed procedure to determine the greatest common factor of fractions 83/76, 478/22, 190/208.

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 83/76,478/22,190/208?

Given fractions are 83/76,478/22,190/208

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 83/76,478/22,190/208, numerators are 83,478,190

Denominators are 76,22,208

The GCF of 83,478,190 is 1 .

LCM of 76,22,208 is 43472.

The greatest common factor of 83/76,478/22,190/208 = [GCF of 83,478,190]/[LCM of 76,22,208]= 1/43472

Therefore, the GCF of 83/76,478/22,190/208 is 1/43472.

Greatest Common Factor of 83,478,190

To find the highest common factor of 83,478,190, we have to find the factors of both numbers and list the highest common factor.

The factors of 83 are 1, 83

The factors of 478 are 1, 2, 239, 478

The factors of 190 are 1, 2, 5, 10, 19, 38, 95, 190

The HCF of 83,478,190 is 1.

Lets's calculate GCF of 83,478,190

Greatest Common Factor (GCF) of 83,478,190 By Common Division

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

Greatest Common Factor of 83,478,190 By Matching Biggest Common Factor Method

Now, list down the factors of 83

1,83

Now, list down the factors of 478

1,2,239,478

Now, list down the factors of 190

1,2,5,10,19,38,95,190

Greatest Common Factor

We found the factors 83,478,190 . The biggest common factor number is the GCF number.
So the greatest common factor 83,478,190 is 1.

Lets's calculate LCM of 76,22,208

Lowest Common Multiple of 76,22,208 using Common Division

2	76, 22, 208
2	38, 11, 104
	19, 11, 52

∴ So the LCM of the given numbers is 2 x 2 x 19 x 11 x 52 = 43472

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43472

Therefore, the GCF of Fractions 83/76,478/22,190/208 is 1/43472

Least Common Multiple of 76,22,208 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 76,22,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(76,22,208) = 2

common factors(in case of two or more numbers have common factors) = 4

GCF(76,22,208) x common factors =2 x 4 = 8

LCM(76,22,208) = ( 76 × 22 × 208 ) / 8

LCM(76,22,208) = 347776 / 8

LCM(76,22,208) = 43472

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FAQs on GCF of Fractions of 83/76, 478/22, 190/208

1. What is the HCF of 83,478,190?

The HCF of 83,478,190 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 83/76, 478/22, 190/208?

Answer: GCF of Numerators as per given numbers 83/76, 478/22, 190/208 is

GCF of Numerators i.e. for 83,478,190 is 1

LCM of denominators i.e. for 76,22,208 is 43472.

Thus, GCF of Fractions is 1/43472.Finally, GCF of Fractions for 83/76, 478/22, 190/208 is 1/43472.