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GCF of 131/414, 584/208

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 131/414, 584/208 i.e 1/43056 easily. The following is the detailed procedure to determine the greatest common factor of fractions 131/414, 584/208.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 131/414,584/208?

Given fractions are 131/414,584/208

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 131/414,584/208, numerators are 131,584

Denominators are 414,208

The GCF of 131,584 is 1 .

LCM of 414,208 is 43056.

The greatest common factor of 131/414,584/208 = [GCF of 131,584]/[LCM of 414,208]= 1/43056

Therefore, the GCF of 131/414,584/208 is 1/43056.

Greatest Common Factor of 131,584

To find the highest common factor of 131,584, we have to find the factors of both numbers and list the highest common factor.

The factors of 131 are 1, 131

The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584

The HCF of 131,584 is 1.

Lets's calculate GCF of 131,584

Greatest Common Factor (GCF) of 131,584 By Common Division

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

Greatest Common Factor of 131,584 By Matching Biggest Common Factor Method

Greatest Common Factor of 131,584 By Matching Biggest Common Factor Method

Now, list down the factors of 131

:

1,131

Now, list down the factors of 584

:

1,2,4,8,73,146,292,584

Greatest Common Factor

We found the factors 131,584 . The biggest common factor number is the GCF number.
So the greatest common factor 131,584 is 1.

Lets's calculate LCM of 414,208

Lowest Common Multiple of 414,208 using Common Division

2 414, 208
207, 104

∴ So the LCM of the given numbers is 2 x 207 x 104 = 43056

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/43056

Therefore, the GCF of Fractions 131/414,584/208 is 1/43056

Least Common Multiple of 414,208 with GCF Formula

Least Common Multiple of 414,208 with GCF Formula

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

We need to calculate greatest common factor of 414,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(414,208) = 2

common factors(in case of two or more numbers have common factors) = 1

GCF(414,208) x common factors =2 x 1 = 2

LCM(414,208) = ( 414 × 208 ) / 2

LCM(414,208) = 86112 / 2

LCM(414,208) = 43056


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FAQs on GCF of Fractions of 131/414, 584/208

1. What is the HCF of 131,584?

The HCF of 131,584 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 131/414, 584/208?

Answer: GCF of Numerators as per given numbers 131/414, 584/208 is

GCF of Numerators i.e. for 131,584 is 1

LCM of denominators i.e. for 414,208 is 43056.

Thus, GCF of Fractions is 1/43056.Finally, GCF of Fractions for 131/414, 584/208 is 1/43056.