How to Find GCF of 77/998, 689/689, 222/468?

GCF of 77/998, 689/689, 222/468

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 77/998, 689/689, 222/468 i.e 1/12377196 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/998, 689/689, 222/468.

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 77/998,689/689,222/468?

Given fractions are 77/998,689/689,222/468

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 77/998,689/689,222/468, numerators are 77,689,222

Denominators are 998,689,468

The GCF of 77,689,222 is 1 .

LCM of 998,689,468 is 12377196.

The greatest common factor of 77/998,689/689,222/468 = [GCF of 77,689,222]/[LCM of 998,689,468]= 1/12377196

Therefore, the GCF of 77/998,689/689,222/468 is 1/12377196.

Greatest Common Factor of 77,689,222

To find the highest common factor of 77,689,222, 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 689 are 1, 13, 53, 689

The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222

The HCF of 77,689,222 is 1.

Lets's calculate GCF of 77,689,222

Greatest Common Factor (GCF) of 77,689,222 By Common Division

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

Greatest Common Factor of 77,689,222 By Matching Biggest Common Factor Method

Now, list down the factors of 77

1,7,11,77

Now, list down the factors of 689

1,13,53,689

Now, list down the factors of 222

1,2,3,6,37,74,111,222

Greatest Common Factor

We found the factors 77,689,222 . The biggest common factor number is the GCF number.
So the greatest common factor 77,689,222 is 1.

Lets's calculate LCM of 998,689,468

Lowest Common Multiple of 998,689,468 using Common Division

2	998, 689, 468
13	499, 689, 234
	499, 53, 18

∴ So the LCM of the given numbers is 2 x 13 x 499 x 53 x 18 = 12377196

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12377196

Therefore, the GCF of Fractions 77/998,689/689,222/468 is 1/12377196

Least Common Multiple of 998,689,468 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 998,689,468 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(998,689,468) = 1

common factors(in case of two or more numbers have common factors) = 26

GCF(998,689,468) x common factors =1 x 26 = 26

LCM(998,689,468) = ( 998 × 689 × 468 ) / 26

LCM(998,689,468) = 321807096 / 26

LCM(998,689,468) = 12377196

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 77/998, 689/689, 222/468

1. What is the HCF of 77,689,222?

The HCF of 77,689,222 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 77/998, 689/689, 222/468?

Answer: GCF of Numerators as per given numbers 77/998, 689/689, 222/468 is

GCF of Numerators i.e. for 77,689,222 is 1

LCM of denominators i.e. for 998,689,468 is 12377196.

Thus, GCF of Fractions is 1/12377196.Finally, GCF of Fractions for 77/998, 689/689, 222/468 is 1/12377196.