How to Find GCF of 82/302, 17/974, 310/912?

GCF of 82/302, 17/974, 310/912

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 82/302, 17/974, 310/912 i.e 1/67065744 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/302, 17/974, 310/912.

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 82/302,17/974,310/912?

Given fractions are 82/302,17/974,310/912

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 82/302,17/974,310/912, numerators are 82,17,310

Denominators are 302,974,912

The GCF of 82,17,310 is 1 .

LCM of 302,974,912 is 67065744.

The greatest common factor of 82/302,17/974,310/912 = [GCF of 82,17,310]/[LCM of 302,974,912]= 1/67065744

Therefore, the GCF of 82/302,17/974,310/912 is 1/67065744.

Greatest Common Factor of 82,17,310

To find the highest common factor of 82,17,310, we have to find the factors of both numbers and list the highest common factor.

The factors of 82 are 1, 2, 41, 82

The factors of 17 are 1, 17

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The HCF of 82,17,310 is 1.

Lets's calculate GCF of 82,17,310

Greatest Common Factor (GCF) of 82,17,310 By Common Division

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

Greatest Common Factor of 82,17,310 By Matching Biggest Common Factor Method

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 17

1,17

Now, list down the factors of 310

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors 82,17,310 . The biggest common factor number is the GCF number.
So the greatest common factor 82,17,310 is 1.

Lets's calculate LCM of 302,974,912

Lowest Common Multiple of 302,974,912 using Common Division

2	302, 974, 912
	151, 487, 456

∴ So the LCM of the given numbers is 2 x 151 x 487 x 456 = 67065744

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/67065744

Therefore, the GCF of Fractions 82/302,17/974,310/912 is 1/67065744

Least Common Multiple of 302,974,912 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 302,974,912 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(302,974,912) = 2

common factors(in case of two or more numbers have common factors) = 2

GCF(302,974,912) x common factors =2 x 2 = 4

LCM(302,974,912) = ( 302 × 974 × 912 ) / 4

LCM(302,974,912) = 268262976 / 4

LCM(302,974,912) = 67065744

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 82/302, 17/974, 310/912

1. What is the HCF of 82,17,310?

The HCF of 82,17,310 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 82/302, 17/974, 310/912?

Answer: GCF of Numerators as per given numbers 82/302, 17/974, 310/912 is

GCF of Numerators i.e. for 82,17,310 is 1

LCM of denominators i.e. for 302,974,912 is 67065744.

Thus, GCF of Fractions is 1/67065744.Finally, GCF of Fractions for 82/302, 17/974, 310/912 is 1/67065744.