How to Find GCF of 490/602, 2003/514?

GCF of 490/602, 2003/514

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 490/602, 2003/514 i.e 1/154714 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/602, 2003/514.

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 490/602,2003/514?

Given fractions are 490/602,2003/514

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 490/602,2003/514, numerators are 490,2003

Denominators are 602,514

The GCF of 490,2003 is 1 .

LCM of 602,514 is 154714.

The greatest common factor of 490/602,2003/514 = [GCF of 490,2003]/[LCM of 602,514]= 1/154714

Therefore, the GCF of 490/602,2003/514 is 1/154714.

Greatest Common Factor of 490,2003

To find the highest common factor of 490,2003, 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 2003 are 1, 2003

The HCF of 490,2003 is 1.

Lets's calculate GCF of 490,2003

Greatest Common Factor (GCF) of 490,2003 By Common Division

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

Greatest Common Factor of 490,2003 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 2003

1,2003

Greatest Common Factor

We found the factors 490,2003 . The biggest common factor number is the GCF number.
So the greatest common factor 490,2003 is 1.

Lets's calculate LCM of 602,514

Lowest Common Multiple of 602,514 using Common Division

2	602, 514
	301, 257

∴ So the LCM of the given numbers is 2 x 301 x 257 = 154714

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/154714

Therefore, the GCF of Fractions 490/602,2003/514 is 1/154714

Least Common Multiple of 602,514 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 602,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(602,514) = 2

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

GCF(602,514) x common factors =2 x 1 = 2

LCM(602,514) = ( 602 × 514 ) / 2

LCM(602,514) = 309428 / 2

LCM(602,514) = 154714

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FAQs on GCF of Fractions of 490/602, 2003/514

1. What is the HCF of 490,2003?

The HCF of 490,2003 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 490/602, 2003/514?

Answer: GCF of Numerators as per given numbers 490/602, 2003/514 is

GCF of Numerators i.e. for 490,2003 is 1

LCM of denominators i.e. for 602,514 is 154714.

Thus, GCF of Fractions is 1/154714.Finally, GCF of Fractions for 490/602, 2003/514 is 1/154714.