How to Find GCF of 1/34, 510/62, 309/81?

GCF of 1/34, 510/62, 309/81

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 1/34, 510/62, 309/81 i.e 1/85374 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1/34, 510/62, 309/81.

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 1/34,510/62,309/81?

Given fractions are 1/34,510/62,309/81

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 1/34,510/62,309/81, numerators are 1,510,309

Denominators are 34,62,81

The GCF of 1,510,309 is 1 .

LCM of 34,62,81 is 85374.

The greatest common factor of 1/34,510/62,309/81 = [GCF of 1,510,309]/[LCM of 34,62,81]= 1/85374

Therefore, the GCF of 1/34,510/62,309/81 is 1/85374.

Greatest Common Factor of 1,510,309

To find the highest common factor of 1,510,309, we have to find the factors of both numbers and list the highest common factor.

The factors of 1 are 1

The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510

The factors of 309 are 1, 3, 103, 309

The HCF of 1,510,309 is 1.

Lets's calculate GCF of 1,510,309

Greatest Common Factor (GCF) of 1,510,309 By Common Division

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

Greatest Common Factor of 1,510,309 By Matching Biggest Common Factor Method

Now, list down the factors of 1

Now, list down the factors of 510

1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510

Now, list down the factors of 309

1,3,103,309

Greatest Common Factor

We found the factors 1,510,309 . The biggest common factor number is the GCF number.
So the greatest common factor 1,510,309 is 1.

Lets's calculate LCM of 34,62,81

Lowest Common Multiple of 34,62,81 using Common Division

2	34, 62, 81
	17, 31, 81

∴ So the LCM of the given numbers is 2 x 17 x 31 x 81 = 85374

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/85374

Therefore, the GCF of Fractions 1/34,510/62,309/81 is 1/85374

Least Common Multiple of 34,62,81 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 34,62,81 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,62,81) = 1

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

GCF(34,62,81) x common factors =1 x 2 = 2

LCM(34,62,81) = ( 34 × 62 × 81 ) / 2

LCM(34,62,81) = 170748 / 2

LCM(34,62,81) = 85374

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FAQs on GCF of Fractions of 1/34, 510/62, 309/81

1. What is the HCF of 1,510,309?

The HCF of 1,510,309 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 1/34, 510/62, 309/81?

Answer: GCF of Numerators as per given numbers 1/34, 510/62, 309/81 is

GCF of Numerators i.e. for 1,510,309 is 1

LCM of denominators i.e. for 34,62,81 is 85374.

Thus, GCF of Fractions is 1/85374.Finally, GCF of Fractions for 1/34, 510/62, 309/81 is 1/85374.