How to Find GCF of 77/61, 84/81, 906/499?

GCF of 77/61, 84/81, 906/499

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 77/61, 84/81, 906/499 i.e 1/2465559 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/61, 84/81, 906/499.

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 77/61,84/81,906/499?

Given fractions are 77/61,84/81,906/499

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 77/61,84/81,906/499, numerators are 77,84,906

Denominators are 61,81,499

The GCF of 77,84,906 is 1 .

LCM of 61,81,499 is 2465559.

The greatest common factor of 77/61,84/81,906/499 = [GCF of 77,84,906]/[LCM of 61,81,499]= 1/2465559

Therefore, the GCF of 77/61,84/81,906/499 is 1/2465559.

Greatest Common Factor of 77,84,906

To find the highest common factor of 77,84,906, 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 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

The factors of 906 are 1, 2, 3, 6, 151, 302, 453, 906

The HCF of 77,84,906 is 1.

Lets's calculate GCF of 77,84,906

Greatest Common Factor (GCF) of 77,84,906 By Common Division

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

Greatest Common Factor of 77,84,906 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 84

1,2,3,4,6,7,12,14,21,28,42,84

Now, list down the factors of 906

1,2,3,6,151,302,453,906

Greatest Common Factor

We found the factors 77,84,906 . The biggest common factor number is the GCF number.
So the greatest common factor 77,84,906 is 1.

Lets's calculate LCM of 61,81,499

Lowest Common Multiple of 61,81,499 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2465559

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2465559

Therefore, the GCF of Fractions 77/61,84/81,906/499 is 1/2465559

Least Common Multiple of 61,81,499 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 61,81,499 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(61,81,499) = 1

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

GCF(61,81,499) x common factors =1 x 1 = 1

LCM(61,81,499) = ( 61 × 81 × 499 ) / 1

LCM(61,81,499) = 2465559 / 1

LCM(61,81,499) = 2465559

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 77/61, 84/81, 906/499

1. What is the HCF of 77,84,906?

The HCF of 77,84,906 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 77/61, 84/81, 906/499?

Answer: GCF of Numerators as per given numbers 77/61, 84/81, 906/499 is

GCF of Numerators i.e. for 77,84,906 is 1

LCM of denominators i.e. for 61,81,499 is 2465559.

Thus, GCF of Fractions is 1/2465559.Finally, GCF of Fractions for 77/61, 84/81, 906/499 is 1/2465559.