How to Find GCF of 29/428, 11/178, 586/564?

GCF of 29/428, 11/178, 586/564

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 29/428, 11/178, 586/564 i.e 1/5370972 easily. The following is the detailed procedure to determine the greatest common factor of fractions 29/428, 11/178, 586/564.

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 29/428,11/178,586/564?

Given fractions are 29/428,11/178,586/564

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 29/428,11/178,586/564, numerators are 29,11,586

Denominators are 428,178,564

The GCF of 29,11,586 is 1 .

LCM of 428,178,564 is 5370972.

The greatest common factor of 29/428,11/178,586/564 = [GCF of 29,11,586]/[LCM of 428,178,564]= 1/5370972

Therefore, the GCF of 29/428,11/178,586/564 is 1/5370972.

Greatest Common Factor of 29,11,586

To find the highest common factor of 29,11,586, we have to find the factors of both numbers and list the highest common factor.

The factors of 29 are 1, 29

The factors of 11 are 1, 11

The factors of 586 are 1, 2, 293, 586

The HCF of 29,11,586 is 1.

Lets's calculate GCF of 29,11,586

Greatest Common Factor (GCF) of 29,11,586 By Common Division

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

Greatest Common Factor of 29,11,586 By Matching Biggest Common Factor Method

Now, list down the factors of 29

1,29

Now, list down the factors of 11

1,11

Now, list down the factors of 586

1,2,293,586

Greatest Common Factor

We found the factors 29,11,586 . The biggest common factor number is the GCF number.
So the greatest common factor 29,11,586 is 1.

Lets's calculate LCM of 428,178,564

Lowest Common Multiple of 428,178,564 using Common Division

2	428, 178, 564
2	214, 89, 282
	107, 89, 141

∴ So the LCM of the given numbers is 2 x 2 x 107 x 89 x 141 = 5370972

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5370972

Therefore, the GCF of Fractions 29/428,11/178,586/564 is 1/5370972

Least Common Multiple of 428,178,564 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 428,178,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(428,178,564) = 2

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

GCF(428,178,564) x common factors =2 x 4 = 8

LCM(428,178,564) = ( 428 × 178 × 564 ) / 8

LCM(428,178,564) = 42967776 / 8

LCM(428,178,564) = 5370972

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FAQs on GCF of Fractions of 29/428, 11/178, 586/564

1. What is the HCF of 29,11,586?

The HCF of 29,11,586 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 29/428, 11/178, 586/564?

Answer: GCF of Numerators as per given numbers 29/428, 11/178, 586/564 is

GCF of Numerators i.e. for 29,11,586 is 1

LCM of denominators i.e. for 428,178,564 is 5370972.

Thus, GCF of Fractions is 1/5370972.Finally, GCF of Fractions for 29/428, 11/178, 586/564 is 1/5370972.