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GCF of 497/409, 208/686

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 497/409, 208/686 i.e 1/280574 easily. The following is the detailed procedure to determine the greatest common factor of fractions 497/409, 208/686.

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 497/409,208/686?

Given fractions are 497/409,208/686

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 497/409,208/686, numerators are 497,208

Denominators are 409,686

The GCF of 497,208 is 1 .

LCM of 409,686 is 280574.

The greatest common factor of 497/409,208/686 = [GCF of 497,208]/[LCM of 409,686]= 1/280574

Therefore, the GCF of 497/409,208/686 is 1/280574.

Greatest Common Factor of 497,208

To find the highest common factor of 497,208, we have to find the factors of both numbers and list the highest common factor.

The factors of 497 are 1, 7, 71, 497

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208

The HCF of 497,208 is 1.

Lets's calculate GCF of 497,208

Greatest Common Factor (GCF) of 497,208 By Common Division

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

Greatest Common Factor of 497,208 By Matching Biggest Common Factor Method

Greatest Common Factor of 497,208 By Matching Biggest Common Factor Method

Now, list down the factors of 497

:

1,7,71,497

Now, list down the factors of 208

:

1,2,4,8,13,16,26,52,104,208

Greatest Common Factor

We found the factors 497,208 . The biggest common factor number is the GCF number.
So the greatest common factor 497,208 is 1.

Lets's calculate LCM of 409,686

Lowest Common Multiple of 409,686 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 280574

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/280574

Therefore, the GCF of Fractions 497/409,208/686 is 1/280574

Least Common Multiple of 409,686 with GCF Formula

Least Common Multiple of 409,686 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 409,686 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(409,686) = 1

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

GCF(409,686) x common factors =1 x 1 = 1

LCM(409,686) = ( 409 × 686 ) / 1

LCM(409,686) = 280574 / 1

LCM(409,686) = 280574


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FAQs on GCF of Fractions of 497/409, 208/686

1. What is the HCF of 497,208?

The HCF of 497,208 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 497/409, 208/686?

Answer: GCF of Numerators as per given numbers 497/409, 208/686 is

GCF of Numerators i.e. for 497,208 is 1

LCM of denominators i.e. for 409,686 is 280574.

Thus, GCF of Fractions is 1/280574.Finally, GCF of Fractions for 497/409, 208/686 is 1/280574.