GCF of 257/175, 994/259
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 257/175, 994/259 i.e 1/6475 easily. The following is the detailed procedure to determine the greatest common factor of fractions 257/175, 994/259.
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 257/175,994/259?
Given fractions are 257/175,994/259
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 257/175,994/259, numerators are 257,994
Denominators are 175,259
The GCF of 257,994 is 1 .
LCM of 175,259 is 6475.
The greatest common factor of 257/175,994/259 = [GCF of 257,994]/[LCM of 175,259]= 1/6475
Therefore, the GCF of 257/175,994/259 is 1/6475.
To find the highest common factor of 257,994, we have to find the factors of both numbers and list the highest common factor.
The factors of 257 are 1, 257
The factors of 994 are 1, 2, 7, 14, 71, 142, 497, 994
The HCF of 257,994 is 1.
Lets's calculate GCF of 257,994
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 257,994 By Matching Biggest Common Factor Method
Now, list down the factors of 257
:1,257
Now, list down the factors of 994
:1,2,7,14,71,142,497,994
Greatest Common Factor
We found the factors 257,994 . The biggest common factor number is the GCF number.
So the greatest common factor 257,994 is 1.
Lets's calculate LCM of 175,259
| 7 | 175, 259 |
| 25, 37 |
∴ So the LCM of the given numbers is 7 x 25 x 37 = 6475
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6475
Therefore, the GCF of Fractions 257/175,994/259 is 1/6475
Least Common Multiple of 175,259 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 175,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(175,259) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(175,259) x common factors =7 x 1 = 7
LCM(175,259) = ( 175 × 259 ) / 7
LCM(175,259) = 45325 / 7
LCM(175,259) = 6475
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FAQs on GCF of Fractions of 257/175, 994/259
1. What is the HCF of 257,994?
The HCF of 257,994 is 1
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 257/175, 994/259?
Answer: GCF of Numerators as per given numbers 257/175, 994/259 is
GCF of Numerators i.e. for 257,994 is 1
LCM of denominators i.e. for 175,259 is 6475.
Thus, GCF of Fractions is 1/6475.Finally, GCF of Fractions for 257/175, 994/259 is 1/6475.