How to Find GCF of 287/141, 2214/7738?

GCF of 287/141, 2214/7738

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 287/141, 2214/7738 i.e 41/1091058 easily. The following is the detailed procedure to determine the greatest common factor of fractions 287/141, 2214/7738.

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 287/141,2214/7738?

Given fractions are 287/141,2214/7738

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 287/141,2214/7738, numerators are 287,2214

Denominators are 141,7738

The GCF of 287,2214 is 41 .

LCM of 141,7738 is 1091058.

The greatest common factor of 287/141,2214/7738 = [GCF of 287,2214]/[LCM of 141,7738]= 41/1091058

Therefore, the GCF of 287/141,2214/7738 is 41/1091058.

Greatest Common Factor of 287,2214

To find the highest common factor of 287,2214, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 2214 are 1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214

The HCF of 287,2214 is 41.

Lets's calculate GCF of 287,2214

Greatest Common Factor (GCF) of 287,2214 By Common Division

41	287, 2214
	7, 54

∴ So the GCF of the given numbers is 41 = 41

Greatest Common Factor of 287,2214 By Matching Biggest Common Factor Method

Now, list down the factors of 287

1,7,41,287

Now, list down the factors of 2214

1,2,3,6,9,18,27,41,54,82,123,246,369,738,1107,2214

Greatest Common Factor

We found the factors 287,2214 . The biggest common factor number is the GCF number.
So the greatest common factor 287,2214 is 41.

Lets's calculate LCM of 141,7738

Lowest Common Multiple of 141,7738 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1091058

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/1091058

Therefore, the GCF of Fractions 287/141,2214/7738 is 41/1091058

Least Common Multiple of 141,7738 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 141,7738 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(141,7738) = 1

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

GCF(141,7738) x common factors =1 x 1 = 1

LCM(141,7738) = ( 141 × 7738 ) / 1

LCM(141,7738) = 1091058 / 1

LCM(141,7738) = 1091058

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FAQs on GCF of Fractions of 287/141, 2214/7738

1. What is the HCF of 287,2214?

The HCF of 287,2214 is 41

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 287/141, 2214/7738?

Answer: GCF of Numerators as per given numbers 287/141, 2214/7738 is

GCF of Numerators i.e. for 287,2214 is 41

LCM of denominators i.e. for 141,7738 is 1091058.

Thus, GCF of Fractions is 41/1091058.Finally, GCF of Fractions for 287/141, 2214/7738 is 41/1091058.