How to Find GCF of 5678/736, 2086/6458?

GCF of 5678/736, 2086/6458

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 5678/736, 2086/6458 i.e 2/2376544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5678/736, 2086/6458.

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 5678/736,2086/6458?

Given fractions are 5678/736,2086/6458

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 5678/736,2086/6458, numerators are 5678,2086

Denominators are 736,6458

The GCF of 5678,2086 is 2 .

LCM of 736,6458 is 2376544.

The greatest common factor of 5678/736,2086/6458 = [GCF of 5678,2086]/[LCM of 736,6458]= 2/2376544

Therefore, the GCF of 5678/736,2086/6458 is 2/2376544.

Greatest Common Factor of 5678,2086

To find the highest common factor of 5678,2086, we have to find the factors of both numbers and list the highest common factor.

The factors of 5678 are 1, 2, 17, 34, 167, 334, 2839, 5678

The factors of 2086 are 1, 2, 7, 14, 149, 298, 1043, 2086

The HCF of 5678,2086 is 2.

Lets's calculate GCF of 5678,2086

Greatest Common Factor (GCF) of 5678,2086 By Common Division

2	5678, 2086
	2839, 1043

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

Greatest Common Factor of 5678,2086 By Matching Biggest Common Factor Method

Now, list down the factors of 5678

1,2,17,34,167,334,2839,5678

Now, list down the factors of 2086

1,2,7,14,149,298,1043,2086

Greatest Common Factor

We found the factors 5678,2086 . The biggest common factor number is the GCF number.
So the greatest common factor 5678,2086 is 2.

Lets's calculate LCM of 736,6458

Lowest Common Multiple of 736,6458 using Common Division

2	736, 6458
	368, 3229

∴ So the LCM of the given numbers is 2 x 368 x 3229 = 2376544

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2376544

Therefore, the GCF of Fractions 5678/736,2086/6458 is 2/2376544

Least Common Multiple of 736,6458 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 736,6458 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(736,6458) = 2

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

GCF(736,6458) x common factors =2 x 1 = 2

LCM(736,6458) = ( 736 × 6458 ) / 2

LCM(736,6458) = 4753088 / 2

LCM(736,6458) = 2376544

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FAQs on GCF of Fractions of 5678/736, 2086/6458

1. What is the HCF of 5678,2086?

The HCF of 5678,2086 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 5678/736, 2086/6458?

Answer: GCF of Numerators as per given numbers 5678/736, 2086/6458 is

GCF of Numerators i.e. for 5678,2086 is 2

LCM of denominators i.e. for 736,6458 is 2376544.

Thus, GCF of Fractions is 2/2376544.Finally, GCF of Fractions for 5678/736, 2086/6458 is 2/2376544.