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GCF of 680/245, 834/306

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 680/245, 834/306 i.e 2/74970 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/245, 834/306.

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 680/245,834/306?

Given fractions are 680/245,834/306

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 680/245,834/306, numerators are 680,834

Denominators are 245,306

The GCF of 680,834 is 2 .

LCM of 245,306 is 74970.

The greatest common factor of 680/245,834/306 = [GCF of 680,834]/[LCM of 245,306]= 2/74970

Therefore, the GCF of 680/245,834/306 is 2/74970.

Greatest Common Factor of 680,834

To find the highest common factor of 680,834, 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 834 are 1, 2, 3, 6, 139, 278, 417, 834

The HCF of 680,834 is 2.

Lets's calculate GCF of 680,834

Greatest Common Factor (GCF) of 680,834 By Common Division

2 680, 834
340, 417

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

Greatest Common Factor of 680,834 By Matching Biggest Common Factor Method

Greatest Common Factor of 680,834 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 834

:

1,2,3,6,139,278,417,834

Greatest Common Factor

We found the factors 680,834 . The biggest common factor number is the GCF number.
So the greatest common factor 680,834 is 2.

Lets's calculate LCM of 245,306

Lowest Common Multiple of 245,306 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 74970

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/74970

Therefore, the GCF of Fractions 680/245,834/306 is 2/74970

Least Common Multiple of 245,306 with GCF Formula

Least Common Multiple of 245,306 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 245,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(245,306) = 1

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

GCF(245,306) x common factors =1 x 1 = 1

LCM(245,306) = ( 245 × 306 ) / 1

LCM(245,306) = 74970 / 1

LCM(245,306) = 74970


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FAQs on GCF of Fractions of 680/245, 834/306

1. What is the HCF of 680,834?

The HCF of 680,834 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 680/245, 834/306?

Answer: GCF of Numerators as per given numbers 680/245, 834/306 is

GCF of Numerators i.e. for 680,834 is 2

LCM of denominators i.e. for 245,306 is 74970.

Thus, GCF of Fractions is 2/74970.Finally, GCF of Fractions for 680/245, 834/306 is 2/74970.