How to Find GCF of 690/729, 198/188?

GCF of 690/729, 198/188

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 690/729, 198/188 i.e 6/137052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 690/729, 198/188.

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 690/729,198/188?

Given fractions are 690/729,198/188

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 690/729,198/188, numerators are 690,198

Denominators are 729,188

The GCF of 690,198 is 6 .

LCM of 729,188 is 137052.

The greatest common factor of 690/729,198/188 = [GCF of 690,198]/[LCM of 729,188]= 6/137052

Therefore, the GCF of 690/729,198/188 is 6/137052.

Greatest Common Factor of 690,198

To find the highest common factor of 690,198, we have to find the factors of both numbers and list the highest common factor.

The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690

The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198

The HCF of 690,198 is 6.

Lets's calculate GCF of 690,198

Greatest Common Factor (GCF) of 690,198 By Common Division

2	690, 198
3	345, 99
	115, 33

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 690,198 By Matching Biggest Common Factor Method

Now, list down the factors of 690

1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690

Now, list down the factors of 198

1,2,3,6,9,11,18,22,33,66,99,198

Greatest Common Factor

We found the factors 690,198 . The biggest common factor number is the GCF number.
So the greatest common factor 690,198 is 6.

Lets's calculate LCM of 729,188

Lowest Common Multiple of 729,188 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 137052

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/137052

Therefore, the GCF of Fractions 690/729,198/188 is 6/137052

Least Common Multiple of 729,188 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 729,188 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(729,188) = 1

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

GCF(729,188) x common factors =1 x 1 = 1

LCM(729,188) = ( 729 × 188 ) / 1

LCM(729,188) = 137052 / 1

LCM(729,188) = 137052

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FAQs on GCF of Fractions of 690/729, 198/188

1. What is the HCF of 690,198?

The HCF of 690,198 is 6

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 690/729, 198/188?

Answer: GCF of Numerators as per given numbers 690/729, 198/188 is

GCF of Numerators i.e. for 690,198 is 6

LCM of denominators i.e. for 729,188 is 137052.

Thus, GCF of Fractions is 6/137052.Finally, GCF of Fractions for 690/729, 198/188 is 6/137052.