How to Find GCF of 77/465, 199/884, 440/998?

GCF of 77/465, 199/884, 440/998

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 77/465, 199/884, 440/998 i.e 1/205118940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/465, 199/884, 440/998.

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 77/465,199/884,440/998?

Given fractions are 77/465,199/884,440/998

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 77/465,199/884,440/998, numerators are 77,199,440

Denominators are 465,884,998

The GCF of 77,199,440 is 1 .

LCM of 465,884,998 is 205118940.

The greatest common factor of 77/465,199/884,440/998 = [GCF of 77,199,440]/[LCM of 465,884,998]= 1/205118940

Therefore, the GCF of 77/465,199/884,440/998 is 1/205118940.

Greatest Common Factor of 77,199,440

To find the highest common factor of 77,199,440, 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 199 are 1, 199

The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440

The HCF of 77,199,440 is 1.

Lets's calculate GCF of 77,199,440

Greatest Common Factor (GCF) of 77,199,440 By Common Division

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

Greatest Common Factor of 77,199,440 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 199

1,199

Now, list down the factors of 440

1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440

Greatest Common Factor

We found the factors 77,199,440 . The biggest common factor number is the GCF number.
So the greatest common factor 77,199,440 is 1.

Lets's calculate LCM of 465,884,998

Lowest Common Multiple of 465,884,998 using Common Division

2	465, 884, 998
	465, 442, 499

∴ So the LCM of the given numbers is 2 x 465 x 442 x 499 = 205118940

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/205118940

Therefore, the GCF of Fractions 77/465,199/884,440/998 is 1/205118940

Least Common Multiple of 465,884,998 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 465,884,998 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(465,884,998) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(465,884,998) x common factors =1 x 2 = 2

LCM(465,884,998) = ( 465 × 884 × 998 ) / 2

LCM(465,884,998) = 410237880 / 2

LCM(465,884,998) = 205118940

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 77/465, 199/884, 440/998

1. What is the HCF of 77,199,440?

The HCF of 77,199,440 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 77/465, 199/884, 440/998?

Answer: GCF of Numerators as per given numbers 77/465, 199/884, 440/998 is

GCF of Numerators i.e. for 77,199,440 is 1

LCM of denominators i.e. for 465,884,998 is 205118940.

Thus, GCF of Fractions is 1/205118940.Finally, GCF of Fractions for 77/465, 199/884, 440/998 is 1/205118940.