How to Find GCF of 490/185, 2778/413?

GCF of 490/185, 2778/413

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 490/185, 2778/413 i.e 2/76405 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/185, 2778/413.

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 490/185,2778/413?

Given fractions are 490/185,2778/413

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 490/185,2778/413, numerators are 490,2778

Denominators are 185,413

The GCF of 490,2778 is 2 .

LCM of 185,413 is 76405.

The greatest common factor of 490/185,2778/413 = [GCF of 490,2778]/[LCM of 185,413]= 2/76405

Therefore, the GCF of 490/185,2778/413 is 2/76405.

Greatest Common Factor of 490,2778

To find the highest common factor of 490,2778, we have to find the factors of both numbers and list the highest common factor.

The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490

The factors of 2778 are 1, 2, 3, 6, 463, 926, 1389, 2778

The HCF of 490,2778 is 2.

Lets's calculate GCF of 490,2778

Greatest Common Factor (GCF) of 490,2778 By Common Division

2	490, 2778
	245, 1389

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

Greatest Common Factor of 490,2778 By Matching Biggest Common Factor Method

Now, list down the factors of 490

1,2,5,7,10,14,35,49,70,98,245,490

Now, list down the factors of 2778

1,2,3,6,463,926,1389,2778

Greatest Common Factor

We found the factors 490,2778 . The biggest common factor number is the GCF number.
So the greatest common factor 490,2778 is 2.

Lets's calculate LCM of 185,413

Lowest Common Multiple of 185,413 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 76405

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/76405

Therefore, the GCF of Fractions 490/185,2778/413 is 2/76405

Least Common Multiple of 185,413 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 185,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(185,413) = 1

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

GCF(185,413) x common factors =1 x 1 = 1

LCM(185,413) = ( 185 × 413 ) / 1

LCM(185,413) = 76405 / 1

LCM(185,413) = 76405

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FAQs on GCF of Fractions of 490/185, 2778/413

1. What is the HCF of 490,2778?

The HCF of 490,2778 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 490/185, 2778/413?

Answer: GCF of Numerators as per given numbers 490/185, 2778/413 is

GCF of Numerators i.e. for 490,2778 is 2

LCM of denominators i.e. for 185,413 is 76405.

Thus, GCF of Fractions is 2/76405.Finally, GCF of Fractions for 490/185, 2778/413 is 2/76405.