How to Find GCF of 209/857, 418/604?

GCF of 209/857, 418/604

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 209/857, 418/604 i.e 209/517628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/857, 418/604.

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 209/857,418/604?

Given fractions are 209/857,418/604

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 209/857,418/604, numerators are 209,418

Denominators are 857,604

The GCF of 209,418 is 209 .

LCM of 857,604 is 517628.

The greatest common factor of 209/857,418/604 = [GCF of 209,418]/[LCM of 857,604]= 209/517628

Therefore, the GCF of 209/857,418/604 is 209/517628.

Greatest Common Factor of 209,418

To find the highest common factor of 209,418, we have to find the factors of both numbers and list the highest common factor.

The factors of 209 are 1, 11, 19, 209

The factors of 418 are 1, 2, 11, 19, 22, 38, 209, 418

The HCF of 209,418 is 209.

Lets's calculate GCF of 209,418

Greatest Common Factor (GCF) of 209,418 By Common Division

11	209, 418
19	19, 38
	1, 2

∴ So the GCF of the given numbers is 11 x 19 = 209

Greatest Common Factor of 209,418 By Matching Biggest Common Factor Method

Now, list down the factors of 209

1,11,19,209

Now, list down the factors of 418

1,2,11,19,22,38,209,418

Greatest Common Factor

We found the factors 209,418 . The biggest common factor number is the GCF number.
So the greatest common factor 209,418 is 209.

Lets's calculate LCM of 857,604

Lowest Common Multiple of 857,604 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 517628

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 209/517628

Therefore, the GCF of Fractions 209/857,418/604 is 209/517628

Least Common Multiple of 857,604 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 857,604 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(857,604) = 1

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

GCF(857,604) x common factors =1 x 1 = 1

LCM(857,604) = ( 857 × 604 ) / 1

LCM(857,604) = 517628 / 1

LCM(857,604) = 517628

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FAQs on GCF of Fractions of 209/857, 418/604

1. What is the HCF of 209,418?

The HCF of 209,418 is 209

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 209/857, 418/604?

Answer: GCF of Numerators as per given numbers 209/857, 418/604 is

GCF of Numerators i.e. for 209,418 is 209

LCM of denominators i.e. for 857,604 is 517628.

Thus, GCF of Fractions is 209/517628.Finally, GCF of Fractions for 209/857, 418/604 is 209/517628.