GCF of 574/198, 1974/514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 574/198, 1974/514 i.e 14/50886 easily. The following is the detailed procedure to determine the greatest common factor of fractions 574/198, 1974/514.
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 574/198,1974/514?
Given fractions are 574/198,1974/514
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 574/198,1974/514, numerators are 574,1974
Denominators are 198,514
The GCF of 574,1974 is 14 .
LCM of 198,514 is 50886.
The greatest common factor of 574/198,1974/514 = [GCF of 574,1974]/[LCM of 198,514]= 14/50886
Therefore, the GCF of 574/198,1974/514 is 14/50886.
To find the highest common factor of 574,1974, we have to find the factors of both numbers and list the highest common factor.
The factors of 574 are 1, 2, 7, 14, 41, 82, 287, 574
The factors of 1974 are 1, 2, 3, 6, 7, 14, 21, 42, 47, 94, 141, 282, 329, 658, 987, 1974
The HCF of 574,1974 is 14.
Lets's calculate GCF of 574,1974
| 2 | 574, 1974 |
| 7 | 287, 987 |
| 41, 141 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 574,1974 By Matching Biggest Common Factor Method
Now, list down the factors of 574
:1,2,7,14,41,82,287,574
Now, list down the factors of 1974
:1,2,3,6,7,14,21,42,47,94,141,282,329,658,987,1974
Greatest Common Factor
We found the factors 574,1974 . The biggest common factor number is the GCF number.
So the greatest common factor 574,1974 is 14.
Lets's calculate LCM of 198,514
| 2 | 198, 514 |
| 99, 257 |
∴ So the LCM of the given numbers is 2 x 99 x 257 = 50886
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/50886
Therefore, the GCF of Fractions 574/198,1974/514 is 14/50886
Least Common Multiple of 198,514 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 198,514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,514) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(198,514) x common factors =2 x 1 = 2
LCM(198,514) = ( 198 × 514 ) / 2
LCM(198,514) = 101772 / 2
LCM(198,514) = 50886
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FAQs on GCF of Fractions of 574/198, 1974/514
1. What is the HCF of 574,1974?
The HCF of 574,1974 is 14
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 574/198, 1974/514?
Answer: GCF of Numerators as per given numbers 574/198, 1974/514 is
GCF of Numerators i.e. for 574,1974 is 14
LCM of denominators i.e. for 198,514 is 50886.
Thus, GCF of Fractions is 14/50886.Finally, GCF of Fractions for 574/198, 1974/514 is 14/50886.