How to Find GCF of 200/49, 688/457?

GCF of 200/49, 688/457

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 200/49, 688/457 i.e 8/22393 easily. The following is the detailed procedure to determine the greatest common factor of fractions 200/49, 688/457.

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 200/49,688/457?

Given fractions are 200/49,688/457

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 200/49,688/457, numerators are 200,688

Denominators are 49,457

The GCF of 200,688 is 8 .

LCM of 49,457 is 22393.

The greatest common factor of 200/49,688/457 = [GCF of 200,688]/[LCM of 49,457]= 8/22393

Therefore, the GCF of 200/49,688/457 is 8/22393.

Greatest Common Factor of 200,688

To find the highest common factor of 200,688, 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 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688

The HCF of 200,688 is 8.

Lets's calculate GCF of 200,688

Greatest Common Factor (GCF) of 200,688 By Common Division

2	200, 688
2	100, 344
2	50, 172
	25, 86

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 200,688 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 688

1,2,4,8,16,43,86,172,344,688

Greatest Common Factor

We found the factors 200,688 . The biggest common factor number is the GCF number.
So the greatest common factor 200,688 is 8.

Lets's calculate LCM of 49,457

Lowest Common Multiple of 49,457 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 22393

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/22393

Therefore, the GCF of Fractions 200/49,688/457 is 8/22393

Least Common Multiple of 49,457 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 49,457 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(49,457) = 1

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

GCF(49,457) x common factors =1 x 1 = 1

LCM(49,457) = ( 49 × 457 ) / 1

LCM(49,457) = 22393 / 1

LCM(49,457) = 22393

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FAQs on GCF of Fractions of 200/49, 688/457

1. What is the HCF of 200,688?

The HCF of 200,688 is 8

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 200/49, 688/457?

Answer: GCF of Numerators as per given numbers 200/49, 688/457 is

GCF of Numerators i.e. for 200,688 is 8

LCM of denominators i.e. for 49,457 is 22393.

Thus, GCF of Fractions is 8/22393.Finally, GCF of Fractions for 200/49, 688/457 is 8/22393.