How to Find GCF of 43/34, 99/31, 308/688?

GCF of 43/34, 99/31, 308/688

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 43/34, 99/31, 308/688 i.e 1/362576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 43/34, 99/31, 308/688.

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 43/34,99/31,308/688?

Given fractions are 43/34,99/31,308/688

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 43/34,99/31,308/688, numerators are 43,99,308

Denominators are 34,31,688

The GCF of 43,99,308 is 1 .

LCM of 34,31,688 is 362576.

The greatest common factor of 43/34,99/31,308/688 = [GCF of 43,99,308]/[LCM of 34,31,688]= 1/362576

Therefore, the GCF of 43/34,99/31,308/688 is 1/362576.

Greatest Common Factor of 43,99,308

To find the highest common factor of 43,99,308, we have to find the factors of both numbers and list the highest common factor.

The factors of 43 are 1, 43

The factors of 99 are 1, 3, 9, 11, 33, 99

The factors of 308 are 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308

The HCF of 43,99,308 is 1.

Lets's calculate GCF of 43,99,308

Greatest Common Factor (GCF) of 43,99,308 By Common Division

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

Greatest Common Factor of 43,99,308 By Matching Biggest Common Factor Method

Now, list down the factors of 43

1,43

Now, list down the factors of 99

1,3,9,11,33,99

Now, list down the factors of 308

1,2,4,7,11,14,22,28,44,77,154,308

Greatest Common Factor

We found the factors 43,99,308 . The biggest common factor number is the GCF number.
So the greatest common factor 43,99,308 is 1.

Lets's calculate LCM of 34,31,688

Lowest Common Multiple of 34,31,688 using Common Division

2	34, 31, 688
	17, 31, 344

∴ So the LCM of the given numbers is 2 x 17 x 31 x 344 = 362576

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/362576

Therefore, the GCF of Fractions 43/34,99/31,308/688 is 1/362576

Least Common Multiple of 34,31,688 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 34,31,688 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,31,688) = 1

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

GCF(34,31,688) x common factors =1 x 2 = 2

LCM(34,31,688) = ( 34 × 31 × 688 ) / 2

LCM(34,31,688) = 725152 / 2

LCM(34,31,688) = 362576

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 43/34, 99/31, 308/688

1. What is the HCF of 43,99,308?

The HCF of 43,99,308 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 43/34, 99/31, 308/688?

Answer: GCF of Numerators as per given numbers 43/34, 99/31, 308/688 is

GCF of Numerators i.e. for 43,99,308 is 1

LCM of denominators i.e. for 34,31,688 is 362576.

Thus, GCF of Fractions is 1/362576.Finally, GCF of Fractions for 43/34, 99/31, 308/688 is 1/362576.