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GCF of 498/13, 310/1253

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 498/13, 310/1253 i.e 2/16289 easily. The following is the detailed procedure to determine the greatest common factor of fractions 498/13, 310/1253.

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 498/13,310/1253?

Given fractions are 498/13,310/1253

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 498/13,310/1253, numerators are 498,310

Denominators are 13,1253

The GCF of 498,310 is 2 .

LCM of 13,1253 is 16289.

The greatest common factor of 498/13,310/1253 = [GCF of 498,310]/[LCM of 13,1253]= 2/16289

Therefore, the GCF of 498/13,310/1253 is 2/16289.

Greatest Common Factor of 498,310

To find the highest common factor of 498,310, we have to find the factors of both numbers and list the highest common factor.

The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The HCF of 498,310 is 2.

Lets's calculate GCF of 498,310

Greatest Common Factor (GCF) of 498,310 By Common Division

2 498, 310
249, 155

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

Greatest Common Factor of 498,310 By Matching Biggest Common Factor Method

Greatest Common Factor of 498,310 By Matching Biggest Common Factor Method

Now, list down the factors of 498

:

1,2,3,6,83,166,249,498

Now, list down the factors of 310

:

1,2,5,10,31,62,155,310

Greatest Common Factor

We found the factors 498,310 . The biggest common factor number is the GCF number.
So the greatest common factor 498,310 is 2.

Lets's calculate LCM of 13,1253

Lowest Common Multiple of 13,1253 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 16289

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/16289

Therefore, the GCF of Fractions 498/13,310/1253 is 2/16289

Least Common Multiple of 13,1253 with GCF Formula

Least Common Multiple of 13,1253 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 13,1253 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(13,1253) = 1

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

GCF(13,1253) x common factors =1 x 1 = 1

LCM(13,1253) = ( 13 × 1253 ) / 1

LCM(13,1253) = 16289 / 1

LCM(13,1253) = 16289


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FAQs on GCF of Fractions of 498/13, 310/1253

1. What is the HCF of 498,310?

The HCF of 498,310 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 498/13, 310/1253?

Answer: GCF of Numerators as per given numbers 498/13, 310/1253 is

GCF of Numerators i.e. for 498,310 is 2

LCM of denominators i.e. for 13,1253 is 16289.

Thus, GCF of Fractions is 2/16289.Finally, GCF of Fractions for 498/13, 310/1253 is 2/16289.