How to Find GCF of 238/187, 700/309?

GCF of 238/187, 700/309

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 238/187, 700/309 i.e 14/57783 easily. The following is the detailed procedure to determine the greatest common factor of fractions 238/187, 700/309.

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 238/187,700/309?

Given fractions are 238/187,700/309

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 238/187,700/309, numerators are 238,700

Denominators are 187,309

The GCF of 238,700 is 14 .

LCM of 187,309 is 57783.

The greatest common factor of 238/187,700/309 = [GCF of 238,700]/[LCM of 187,309]= 14/57783

Therefore, the GCF of 238/187,700/309 is 14/57783.

Greatest Common Factor of 238,700

To find the highest common factor of 238,700, we have to find the factors of both numbers and list the highest common factor.

The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

The HCF of 238,700 is 14.

Lets's calculate GCF of 238,700

Greatest Common Factor (GCF) of 238,700 By Common Division

2	238, 700
7	119, 350
	17, 50

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 238,700 By Matching Biggest Common Factor Method

Now, list down the factors of 238

1,2,7,14,17,34,119,238

Now, list down the factors of 700

1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700

Greatest Common Factor

We found the factors 238,700 . The biggest common factor number is the GCF number.
So the greatest common factor 238,700 is 14.

Lets's calculate LCM of 187,309

Lowest Common Multiple of 187,309 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 57783

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/57783

Therefore, the GCF of Fractions 238/187,700/309 is 14/57783

Least Common Multiple of 187,309 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 187,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(187,309) = 1

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

GCF(187,309) x common factors =1 x 1 = 1

LCM(187,309) = ( 187 × 309 ) / 1

LCM(187,309) = 57783 / 1

LCM(187,309) = 57783

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FAQs on GCF of Fractions of 238/187, 700/309

1. What is the HCF of 238,700?

The HCF of 238,700 is 14

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 238/187, 700/309?

Answer: GCF of Numerators as per given numbers 238/187, 700/309 is

GCF of Numerators i.e. for 238,700 is 14

LCM of denominators i.e. for 187,309 is 57783.

Thus, GCF of Fractions is 14/57783.Finally, GCF of Fractions for 238/187, 700/309 is 14/57783.