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GCF of 198/321, 969/943

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 198/321, 969/943 i.e 3/302703 easily. The following is the detailed procedure to determine the greatest common factor of fractions 198/321, 969/943.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 198/321,969/943?

Given fractions are 198/321,969/943

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 198/321,969/943, numerators are 198,969

Denominators are 321,943

The GCF of 198,969 is 3 .

LCM of 321,943 is 302703.

The greatest common factor of 198/321,969/943 = [GCF of 198,969]/[LCM of 321,943]= 3/302703

Therefore, the GCF of 198/321,969/943 is 3/302703.

Greatest Common Factor of 198,969

To find the highest common factor of 198,969, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969

The HCF of 198,969 is 3.

Lets's calculate GCF of 198,969

Greatest Common Factor (GCF) of 198,969 By Common Division

3 198, 969
66, 323

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 198,969 By Matching Biggest Common Factor Method

Greatest Common Factor of 198,969 By Matching Biggest Common Factor Method

Now, list down the factors of 198

:

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

Now, list down the factors of 969

:

1,3,17,19,51,57,323,969

Greatest Common Factor

We found the factors 198,969 . The biggest common factor number is the GCF number.
So the greatest common factor 198,969 is 3.

Lets's calculate LCM of 321,943

Lowest Common Multiple of 321,943 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 302703

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/302703

Therefore, the GCF of Fractions 198/321,969/943 is 3/302703

Least Common Multiple of 321,943 with GCF Formula

Least Common Multiple of 321,943 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 321,943 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(321,943) = 1

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

GCF(321,943) x common factors =1 x 1 = 1

LCM(321,943) = ( 321 × 943 ) / 1

LCM(321,943) = 302703 / 1

LCM(321,943) = 302703


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FAQs on GCF of Fractions of 198/321, 969/943

1. What is the HCF of 198,969?

The HCF of 198,969 is 3

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 198/321, 969/943?

Answer: GCF of Numerators as per given numbers 198/321, 969/943 is

GCF of Numerators i.e. for 198,969 is 3

LCM of denominators i.e. for 321,943 is 302703.

Thus, GCF of Fractions is 3/302703.Finally, GCF of Fractions for 198/321, 969/943 is 3/302703.