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GCF of 34/58, 38/81, 112/310

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 34/58, 38/81, 112/310 i.e 2/728190 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/58, 38/81, 112/310.

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 34/58,38/81,112/310?

Given fractions are 34/58,38/81,112/310

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 34/58,38/81,112/310, numerators are 34,38,112

Denominators are 58,81,310

The GCF of 34,38,112 is 2 .

LCM of 58,81,310 is 728190.

The greatest common factor of 34/58,38/81,112/310 = [GCF of 34,38,112]/[LCM of 58,81,310]= 2/728190

Therefore, the GCF of 34/58,38/81,112/310 is 2/728190.

Greatest Common Factor of 34,38,112

To find the highest common factor of 34,38,112, we have to find the factors of both numbers and list the highest common factor.

The factors of 34 are 1, 2, 17, 34

The factors of 38 are 1, 2, 19, 38

The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

The HCF of 34,38,112 is 2.

Lets's calculate GCF of 34,38,112

Greatest Common Factor (GCF) of 34,38,112 By Common Division

2 34, 38, 112
17, 19, 56

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 34,38,112 By Matching Biggest Common Factor Method

Greatest Common Factor of 34,38,112 By Matching Biggest Common Factor Method

Now, list down the factors of 34

:

1,2,17,34

Now, list down the factors of 38

:

1,2,19,38

Now, list down the factors of 112

:

1,2,4,7,8,14,16,28,56,112

Greatest Common Factor

We found the factors 34,38,112 . The biggest common factor number is the GCF number.
So the greatest common factor 34,38,112 is 2.


Lets's calculate LCM of 58,81,310

Lowest Common Multiple of 58,81,310 using Common Division

2 58, 81, 310
29, 81, 155

∴ So the LCM of the given numbers is 2 x 29 x 81 x 155 = 728190

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/728190

Therefore, the GCF of Fractions 34/58,38/81,112/310 is 2/728190

Least Common Multiple of 58,81,310 with GCF Formula

Least Common Multiple of 58,81,310 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 58,81,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(58,81,310) = 1

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

GCF(58,81,310) x common factors =1 x 2 = 2

LCM(58,81,310) = ( 58 × 81 × 310 ) / 2

LCM(58,81,310) = 1456380 / 2

LCM(58,81,310) = 728190


GCF of Fractions Calculation Examples

FAQs on GCF of Fractions of 34/58, 38/81, 112/310

1. What is the HCF of 34,38,112?

The HCF of 34,38,112 is 2

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 34/58, 38/81, 112/310?

Answer: GCF of Numerators as per given numbers 34/58, 38/81, 112/310 is

GCF of Numerators i.e. for 34,38,112 is 2

LCM of denominators i.e. for 58,81,310 is 728190.

Thus, GCF of Fractions is 2/728190.Finally, GCF of Fractions for 34/58, 38/81, 112/310 is 2/728190.