GCF of 310/259, 259/749
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 310/259, 259/749 i.e 1/27713 easily. The following is the detailed procedure to determine the greatest common factor of fractions 310/259, 259/749.
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 310/259,259/749?
Given fractions are 310/259,259/749
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 310/259,259/749, numerators are 310,259
Denominators are 259,749
The GCF of 310,259 is 1 .
LCM of 259,749 is 27713.
The greatest common factor of 310/259,259/749 = [GCF of 310,259]/[LCM of 259,749]= 1/27713
Therefore, the GCF of 310/259,259/749 is 1/27713.
To find the highest common factor of 310,259, we have to find the factors of both numbers and list the highest common factor.
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The factors of 259 are 1, 7, 37, 259
The HCF of 310,259 is 1.
Lets's calculate GCF of 310,259
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 310,259 By Matching Biggest Common Factor Method
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Now, list down the factors of 259
:1,7,37,259
Greatest Common Factor
We found the factors 310,259 . The biggest common factor number is the GCF number.
So the greatest common factor 310,259 is 1.
Lets's calculate LCM of 259,749
| 7 | 259, 749 |
| 37, 107 |
∴ So the LCM of the given numbers is 7 x 37 x 107 = 27713
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27713
Therefore, the GCF of Fractions 310/259,259/749 is 1/27713
Least Common Multiple of 259,749 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 259,749 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(259,749) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(259,749) x common factors =7 x 1 = 7
LCM(259,749) = ( 259 × 749 ) / 7
LCM(259,749) = 193991 / 7
LCM(259,749) = 27713
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FAQs on GCF of Fractions of 310/259, 259/749
1. What is the HCF of 310,259?
The HCF of 310,259 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 310/259, 259/749?
Answer: GCF of Numerators as per given numbers 310/259, 259/749 is
GCF of Numerators i.e. for 310,259 is 1
LCM of denominators i.e. for 259,749 is 27713.
Thus, GCF of Fractions is 1/27713.Finally, GCF of Fractions for 310/259, 259/749 is 1/27713.