How to Find GCF of 198/83, 312/4754?

GCF of 198/83, 312/4754

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 198/83, 312/4754 i.e 6/394582 easily. The following is the detailed procedure to determine the greatest common factor of fractions 198/83, 312/4754.

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 198/83,312/4754?

Given fractions are 198/83,312/4754

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 198/83,312/4754, numerators are 198,312

Denominators are 83,4754

The GCF of 198,312 is 6 .

LCM of 83,4754 is 394582.

The greatest common factor of 198/83,312/4754 = [GCF of 198,312]/[LCM of 83,4754]= 6/394582

Therefore, the GCF of 198/83,312/4754 is 6/394582.

Greatest Common Factor of 198,312

To find the highest common factor of 198,312, 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 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312

The HCF of 198,312 is 6.

Lets's calculate GCF of 198,312

Greatest Common Factor (GCF) of 198,312 By Common Division

2	198, 312
3	99, 156
	33, 52

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

Greatest Common Factor of 198,312 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 312

1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312

Greatest Common Factor

We found the factors 198,312 . The biggest common factor number is the GCF number.
So the greatest common factor 198,312 is 6.

Lets's calculate LCM of 83,4754

Lowest Common Multiple of 83,4754 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 394582

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/394582

Therefore, the GCF of Fractions 198/83,312/4754 is 6/394582

Least Common Multiple of 83,4754 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 83,4754 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(83,4754) = 1

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

GCF(83,4754) x common factors =1 x 1 = 1

LCM(83,4754) = ( 83 × 4754 ) / 1

LCM(83,4754) = 394582 / 1

LCM(83,4754) = 394582

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FAQs on GCF of Fractions of 198/83, 312/4754

1. What is the HCF of 198,312?

The HCF of 198,312 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 198/83, 312/4754?

Answer: GCF of Numerators as per given numbers 198/83, 312/4754 is

GCF of Numerators i.e. for 198,312 is 6

LCM of denominators i.e. for 83,4754 is 394582.

Thus, GCF of Fractions is 6/394582.Finally, GCF of Fractions for 198/83, 312/4754 is 6/394582.