How to Find GCF of 200/293, 680/558?

GCF of 200/293, 680/558

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 200/293, 680/558 i.e 40/163494 easily. The following is the detailed procedure to determine the greatest common factor of fractions 200/293, 680/558.

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 200/293,680/558?

Given fractions are 200/293,680/558

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 200/293,680/558, numerators are 200,680

Denominators are 293,558

The GCF of 200,680 is 40 .

LCM of 293,558 is 163494.

The greatest common factor of 200/293,680/558 = [GCF of 200,680]/[LCM of 293,558]= 40/163494

Therefore, the GCF of 200/293,680/558 is 40/163494.

Greatest Common Factor of 200,680

To find the highest common factor of 200,680, we have to find the factors of both numbers and list the highest common factor.

The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680

The HCF of 200,680 is 40.

Lets's calculate GCF of 200,680

Greatest Common Factor (GCF) of 200,680 By Common Division

2	200, 680
2	100, 340
2	50, 170
5	25, 85
	5, 17

∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40

Greatest Common Factor of 200,680 By Matching Biggest Common Factor Method

Now, list down the factors of 200

1,2,4,5,8,10,20,25,40,50,100,200

Now, list down the factors of 680

1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680

Greatest Common Factor

We found the factors 200,680 . The biggest common factor number is the GCF number.
So the greatest common factor 200,680 is 40.

Lets's calculate LCM of 293,558

Lowest Common Multiple of 293,558 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 163494

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/163494

Therefore, the GCF of Fractions 200/293,680/558 is 40/163494

Least Common Multiple of 293,558 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 293,558 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(293,558) = 1

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

GCF(293,558) x common factors =1 x 1 = 1

LCM(293,558) = ( 293 × 558 ) / 1

LCM(293,558) = 163494 / 1

LCM(293,558) = 163494

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FAQs on GCF of Fractions of 200/293, 680/558

1. What is the HCF of 200,680?

The HCF of 200,680 is 40

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 200/293, 680/558?

Answer: GCF of Numerators as per given numbers 200/293, 680/558 is

GCF of Numerators i.e. for 200,680 is 40

LCM of denominators i.e. for 293,558 is 163494.

Thus, GCF of Fractions is 40/163494.Finally, GCF of Fractions for 200/293, 680/558 is 40/163494.