How to Find GCF of 680/179, 830/394?

GCF of 680/179, 830/394

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 680/179, 830/394 i.e 10/70526 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/179, 830/394.

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 680/179,830/394?

Given fractions are 680/179,830/394

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 680/179,830/394, numerators are 680,830

Denominators are 179,394

The GCF of 680,830 is 10 .

LCM of 179,394 is 70526.

The greatest common factor of 680/179,830/394 = [GCF of 680,830]/[LCM of 179,394]= 10/70526

Therefore, the GCF of 680/179,830/394 is 10/70526.

Greatest Common Factor of 680,830

To find the highest common factor of 680,830, we have to find the factors of both numbers and list the highest common factor.

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830

The HCF of 680,830 is 10.

Lets's calculate GCF of 680,830

Greatest Common Factor (GCF) of 680,830 By Common Division

2	680, 830
5	340, 415
	68, 83

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 680,830 By Matching Biggest Common Factor Method

Now, list down the factors of 680

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

Now, list down the factors of 830

1,2,5,10,83,166,415,830

Greatest Common Factor

We found the factors 680,830 . The biggest common factor number is the GCF number.
So the greatest common factor 680,830 is 10.

Lets's calculate LCM of 179,394

Lowest Common Multiple of 179,394 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 70526

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/70526

Therefore, the GCF of Fractions 680/179,830/394 is 10/70526

Least Common Multiple of 179,394 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 179,394 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(179,394) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(179,394) x common factors =1 x 1 = 1

LCM(179,394) = ( 179 × 394 ) / 1

LCM(179,394) = 70526 / 1

LCM(179,394) = 70526

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FAQs on GCF of Fractions of 680/179, 830/394

1. What is the HCF of 680,830?

The HCF of 680,830 is 10

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 680/179, 830/394?

Answer: GCF of Numerators as per given numbers 680/179, 830/394 is

GCF of Numerators i.e. for 680,830 is 10

LCM of denominators i.e. for 179,394 is 70526.

Thus, GCF of Fractions is 10/70526.Finally, GCF of Fractions for 680/179, 830/394 is 10/70526.