How to Find GCF of 61/29, 301/36, 506/472?

GCF of 61/29, 301/36, 506/472

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 61/29, 301/36, 506/472 i.e 1/123192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 61/29, 301/36, 506/472.

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 61/29,301/36,506/472?

Given fractions are 61/29,301/36,506/472

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 61/29,301/36,506/472, numerators are 61,301,506

Denominators are 29,36,472

The GCF of 61,301,506 is 1 .

LCM of 29,36,472 is 123192.

The greatest common factor of 61/29,301/36,506/472 = [GCF of 61,301,506]/[LCM of 29,36,472]= 1/123192

Therefore, the GCF of 61/29,301/36,506/472 is 1/123192.

Greatest Common Factor of 61,301,506

To find the highest common factor of 61,301,506, we have to find the factors of both numbers and list the highest common factor.

The factors of 61 are 1, 61

The factors of 301 are 1, 7, 43, 301

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The HCF of 61,301,506 is 1.

Lets's calculate GCF of 61,301,506

Greatest Common Factor (GCF) of 61,301,506 By Common Division

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

Greatest Common Factor of 61,301,506 By Matching Biggest Common Factor Method

Now, list down the factors of 61

1,61

Now, list down the factors of 301

1,7,43,301

Now, list down the factors of 506

1,2,11,22,23,46,253,506

Greatest Common Factor

We found the factors 61,301,506 . The biggest common factor number is the GCF number.
So the greatest common factor 61,301,506 is 1.

Lets's calculate LCM of 29,36,472

Lowest Common Multiple of 29,36,472 using Common Division

2	29, 36, 472
2	29, 18, 236
	29, 9, 118

∴ So the LCM of the given numbers is 2 x 2 x 29 x 9 x 118 = 123192

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/123192

Therefore, the GCF of Fractions 61/29,301/36,506/472 is 1/123192

Least Common Multiple of 29,36,472 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 29,36,472 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(29,36,472) = 1

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

GCF(29,36,472) x common factors =1 x 4 = 4

LCM(29,36,472) = ( 29 × 36 × 472 ) / 4

LCM(29,36,472) = 492768 / 4

LCM(29,36,472) = 123192

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FAQs on GCF of Fractions of 61/29, 301/36, 506/472

1. What is the HCF of 61,301,506?

The HCF of 61,301,506 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 61/29, 301/36, 506/472?

Answer: GCF of Numerators as per given numbers 61/29, 301/36, 506/472 is

GCF of Numerators i.e. for 61,301,506 is 1

LCM of denominators i.e. for 29,36,472 is 123192.

Thus, GCF of Fractions is 1/123192.Finally, GCF of Fractions for 61/29, 301/36, 506/472 is 1/123192.