How to Find GCF of 8678/298, 5627/7838?

GCF of 8678/298, 5627/7838

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 8678/298, 5627/7838 i.e 1/1167862 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8678/298, 5627/7838.

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 8678/298,5627/7838?

Given fractions are 8678/298,5627/7838

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 8678/298,5627/7838, numerators are 8678,5627

Denominators are 298,7838

The GCF of 8678,5627 is 1 .

LCM of 298,7838 is 1167862.

The greatest common factor of 8678/298,5627/7838 = [GCF of 8678,5627]/[LCM of 298,7838]= 1/1167862

Therefore, the GCF of 8678/298,5627/7838 is 1/1167862.

Greatest Common Factor of 8678,5627

To find the highest common factor of 8678,5627, we have to find the factors of both numbers and list the highest common factor.

The factors of 8678 are 1, 2, 4339, 8678

The factors of 5627 are 1, 17, 331, 5627

The HCF of 8678,5627 is 1.

Lets's calculate GCF of 8678,5627

Greatest Common Factor (GCF) of 8678,5627 By Common Division

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

Greatest Common Factor of 8678,5627 By Matching Biggest Common Factor Method

Now, list down the factors of 8678

1,2,4339,8678

Now, list down the factors of 5627

1,17,331,5627

Greatest Common Factor

We found the factors 8678,5627 . The biggest common factor number is the GCF number.
So the greatest common factor 8678,5627 is 1.

Lets's calculate LCM of 298,7838

Lowest Common Multiple of 298,7838 using Common Division

2	298, 7838
	149, 3919

∴ So the LCM of the given numbers is 2 x 149 x 3919 = 1167862

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1167862

Therefore, the GCF of Fractions 8678/298,5627/7838 is 1/1167862

Least Common Multiple of 298,7838 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 298,7838 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(298,7838) = 2

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

GCF(298,7838) x common factors =2 x 1 = 2

LCM(298,7838) = ( 298 × 7838 ) / 2

LCM(298,7838) = 2335724 / 2

LCM(298,7838) = 1167862

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 8678/298, 5627/7838

1. What is the HCF of 8678,5627?

The HCF of 8678,5627 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 8678/298, 5627/7838?

Answer: GCF of Numerators as per given numbers 8678/298, 5627/7838 is

GCF of Numerators i.e. for 8678,5627 is 1

LCM of denominators i.e. for 298,7838 is 1167862.

Thus, GCF of Fractions is 1/1167862.Finally, GCF of Fractions for 8678/298, 5627/7838 is 1/1167862.