How to Find GCF of 8662/257, 3716/413?

GCF of 8662/257, 3716/413

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 8662/257, 3716/413 i.e 2/106141 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8662/257, 3716/413.

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 8662/257,3716/413?

Given fractions are 8662/257,3716/413

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 8662/257,3716/413, numerators are 8662,3716

Denominators are 257,413

The GCF of 8662,3716 is 2 .

LCM of 257,413 is 106141.

The greatest common factor of 8662/257,3716/413 = [GCF of 8662,3716]/[LCM of 257,413]= 2/106141

Therefore, the GCF of 8662/257,3716/413 is 2/106141.

Greatest Common Factor of 8662,3716

To find the highest common factor of 8662,3716, we have to find the factors of both numbers and list the highest common factor.

The factors of 8662 are 1, 2, 61, 71, 122, 142, 4331, 8662

The factors of 3716 are 1, 2, 4, 929, 1858, 3716

The HCF of 8662,3716 is 2.

Lets's calculate GCF of 8662,3716

Greatest Common Factor (GCF) of 8662,3716 By Common Division

2	8662, 3716
	4331, 1858

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

Greatest Common Factor of 8662,3716 By Matching Biggest Common Factor Method

Now, list down the factors of 8662

1,2,61,71,122,142,4331,8662

Now, list down the factors of 3716

1,2,4,929,1858,3716

Greatest Common Factor

We found the factors 8662,3716 . The biggest common factor number is the GCF number.
So the greatest common factor 8662,3716 is 2.

Lets's calculate LCM of 257,413

Lowest Common Multiple of 257,413 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 106141

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/106141

Therefore, the GCF of Fractions 8662/257,3716/413 is 2/106141

Least Common Multiple of 257,413 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 257,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(257,413) = 1

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

GCF(257,413) x common factors =1 x 1 = 1

LCM(257,413) = ( 257 × 413 ) / 1

LCM(257,413) = 106141 / 1

LCM(257,413) = 106141

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FAQs on GCF of Fractions of 8662/257, 3716/413

1. What is the HCF of 8662,3716?

The HCF of 8662,3716 is 2

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 8662/257, 3716/413?

Answer: GCF of Numerators as per given numbers 8662/257, 3716/413 is

GCF of Numerators i.e. for 8662,3716 is 2

LCM of denominators i.e. for 257,413 is 106141.

Thus, GCF of Fractions is 2/106141.Finally, GCF of Fractions for 8662/257, 3716/413 is 2/106141.