How to Find GCF of 77/87, 91/90, 189/622?

GCF of 77/87, 91/90, 189/622

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 77/87, 91/90, 189/622 i.e 7/811710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/87, 91/90, 189/622.

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 77/87,91/90,189/622?

Given fractions are 77/87,91/90,189/622

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 77/87,91/90,189/622, numerators are 77,91,189

Denominators are 87,90,622

The GCF of 77,91,189 is 7 .

LCM of 87,90,622 is 811710.

The greatest common factor of 77/87,91/90,189/622 = [GCF of 77,91,189]/[LCM of 87,90,622]= 7/811710

Therefore, the GCF of 77/87,91/90,189/622 is 7/811710.

Greatest Common Factor of 77,91,189

To find the highest common factor of 77,91,189, we have to find the factors of both numbers and list the highest common factor.

The factors of 77 are 1, 7, 11, 77

The factors of 91 are 1, 7, 13, 91

The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189

The HCF of 77,91,189 is 7.

Lets's calculate GCF of 77,91,189

Greatest Common Factor (GCF) of 77,91,189 By Common Division

7	77, 91, 189
	11, 13, 27

∴ So the GCF of the given numbers is 7 = 7

Greatest Common Factor of 77,91,189 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 91

1,7,13,91

Now, list down the factors of 189

1,3,7,9,21,27,63,189

Greatest Common Factor

We found the factors 77,91,189 . The biggest common factor number is the GCF number.
So the greatest common factor 77,91,189 is 7.

Lets's calculate LCM of 87,90,622

Lowest Common Multiple of 87,90,622 using Common Division

2	87, 90, 622
3	87, 45, 311
	29, 15, 311

∴ So the LCM of the given numbers is 2 x 3 x 29 x 15 x 311 = 811710

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/811710

Therefore, the GCF of Fractions 77/87,91/90,189/622 is 7/811710

Least Common Multiple of 87,90,622 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 87,90,622 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(87,90,622) = 1

common factors(in case of two or more numbers have common factors) = 6

GCF(87,90,622) x common factors =1 x 6 = 6

LCM(87,90,622) = ( 87 × 90 × 622 ) / 6

LCM(87,90,622) = 4870260 / 6

LCM(87,90,622) = 811710

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 77/87, 91/90, 189/622

1. What is the HCF of 77,91,189?

The HCF of 77,91,189 is 7

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 77/87, 91/90, 189/622?

Answer: GCF of Numerators as per given numbers 77/87, 91/90, 189/622 is

GCF of Numerators i.e. for 77,91,189 is 7

LCM of denominators i.e. for 87,90,622 is 811710.

Thus, GCF of Fractions is 7/811710.Finally, GCF of Fractions for 77/87, 91/90, 189/622 is 7/811710.