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GCF of 380/314, 287/209

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 380/314, 287/209 i.e 1/65626 easily. The following is the detailed procedure to determine the greatest common factor of fractions 380/314, 287/209.

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 380/314,287/209?

Given fractions are 380/314,287/209

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 380/314,287/209, numerators are 380,287

Denominators are 314,209

The GCF of 380,287 is 1 .

LCM of 314,209 is 65626.

The greatest common factor of 380/314,287/209 = [GCF of 380,287]/[LCM of 314,209]= 1/65626

Therefore, the GCF of 380/314,287/209 is 1/65626.

Greatest Common Factor of 380,287

To find the highest common factor of 380,287, we have to find the factors of both numbers and list the highest common factor.

The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

The factors of 287 are 1, 7, 41, 287

The HCF of 380,287 is 1.

Lets's calculate GCF of 380,287

Greatest Common Factor (GCF) of 380,287 By Common Division

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

Greatest Common Factor of 380,287 By Matching Biggest Common Factor Method

Greatest Common Factor of 380,287 By Matching Biggest Common Factor Method

Now, list down the factors of 380

:

1,2,4,5,10,19,20,38,76,95,190,380

Now, list down the factors of 287

:

1,7,41,287

Greatest Common Factor

We found the factors 380,287 . The biggest common factor number is the GCF number.
So the greatest common factor 380,287 is 1.

Lets's calculate LCM of 314,209

Lowest Common Multiple of 314,209 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 65626

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/65626

Therefore, the GCF of Fractions 380/314,287/209 is 1/65626

Least Common Multiple of 314,209 with GCF Formula

Least Common Multiple of 314,209 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 314,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(314,209) = 1

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

GCF(314,209) x common factors =1 x 1 = 1

LCM(314,209) = ( 314 × 209 ) / 1

LCM(314,209) = 65626 / 1

LCM(314,209) = 65626


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FAQs on GCF of Fractions of 380/314, 287/209

1. What is the HCF of 380,287?

The HCF of 380,287 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 380/314, 287/209?

Answer: GCF of Numerators as per given numbers 380/314, 287/209 is

GCF of Numerators i.e. for 380,287 is 1

LCM of denominators i.e. for 314,209 is 65626.

Thus, GCF of Fractions is 1/65626.Finally, GCF of Fractions for 380/314, 287/209 is 1/65626.