How to Find GCF of 490/320, 1991/312?

GCF of 490/320, 1991/312

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 490/320, 1991/312 i.e 1/12480 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/320, 1991/312.

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 490/320,1991/312?

Given fractions are 490/320,1991/312

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 490/320,1991/312, numerators are 490,1991

Denominators are 320,312

The GCF of 490,1991 is 1 .

LCM of 320,312 is 12480.

The greatest common factor of 490/320,1991/312 = [GCF of 490,1991]/[LCM of 320,312]= 1/12480

Therefore, the GCF of 490/320,1991/312 is 1/12480.

Greatest Common Factor of 490,1991

To find the highest common factor of 490,1991, 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 1991 are 1, 11, 181, 1991

The HCF of 490,1991 is 1.

Lets's calculate GCF of 490,1991

Greatest Common Factor (GCF) of 490,1991 By Common Division

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

Greatest Common Factor of 490,1991 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 1991

1,11,181,1991

Greatest Common Factor

We found the factors 490,1991 . The biggest common factor number is the GCF number.
So the greatest common factor 490,1991 is 1.

Lets's calculate LCM of 320,312

Lowest Common Multiple of 320,312 using Common Division

2	320, 312
2	160, 156
2	80, 78
	40, 39

∴ So the LCM of the given numbers is 2 x 2 x 2 x 40 x 39 = 12480

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12480

Therefore, the GCF of Fractions 490/320,1991/312 is 1/12480

Least Common Multiple of 320,312 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 320,312 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(320,312) = 8

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

GCF(320,312) x common factors =8 x 1 = 8

LCM(320,312) = ( 320 × 312 ) / 8

LCM(320,312) = 99840 / 8

LCM(320,312) = 12480

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FAQs on GCF of Fractions of 490/320, 1991/312

1. What is the HCF of 490,1991?

The HCF of 490,1991 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 490/320, 1991/312?

Answer: GCF of Numerators as per given numbers 490/320, 1991/312 is

GCF of Numerators i.e. for 490,1991 is 1

LCM of denominators i.e. for 320,312 is 12480.

Thus, GCF of Fractions is 1/12480.Finally, GCF of Fractions for 490/320, 1991/312 is 1/12480.