GCF of 574/590, 742/200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 574/590, 742/200 i.e 14/11800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 574/590, 742/200.
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 574/590,742/200?
Given fractions are 574/590,742/200
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 574/590,742/200, numerators are 574,742
Denominators are 590,200
The GCF of 574,742 is 14 .
LCM of 590,200 is 11800.
The greatest common factor of 574/590,742/200 = [GCF of 574,742]/[LCM of 590,200]= 14/11800
Therefore, the GCF of 574/590,742/200 is 14/11800.
To find the highest common factor of 574,742, 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 742 are 1, 2, 7, 14, 53, 106, 371, 742
The HCF of 574,742 is 14.
Lets's calculate GCF of 574,742
| 2 | 574, 742 |
| 7 | 287, 371 |
| 41, 53 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 574,742 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 742
:1,2,7,14,53,106,371,742
Greatest Common Factor
We found the factors 574,742 . The biggest common factor number is the GCF number.
So the greatest common factor 574,742 is 14.
Lets's calculate LCM of 590,200
| 2 | 590, 200 |
| 5 | 295, 100 |
| 59, 20 |
∴ So the LCM of the given numbers is 2 x 5 x 59 x 20 = 11800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/11800
Therefore, the GCF of Fractions 574/590,742/200 is 14/11800
Least Common Multiple of 590,200 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 590,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(590,200) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(590,200) x common factors =10 x 1 = 10
LCM(590,200) = ( 590 × 200 ) / 10
LCM(590,200) = 118000 / 10
LCM(590,200) = 11800
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FAQs on GCF of Fractions of 574/590, 742/200
1. What is the HCF of 574,742?
The HCF of 574,742 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 574/590, 742/200?
Answer: GCF of Numerators as per given numbers 574/590, 742/200 is
GCF of Numerators i.e. for 574,742 is 14
LCM of denominators i.e. for 590,200 is 11800.
Thus, GCF of Fractions is 14/11800.Finally, GCF of Fractions for 574/590, 742/200 is 14/11800.