GCF of 875/257, 810/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 875/257, 810/314 i.e 5/80698 easily. The following is the detailed procedure to determine the greatest common factor of fractions 875/257, 810/314.
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 875/257,810/314?
Given fractions are 875/257,810/314
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 875/257,810/314, numerators are 875,810
Denominators are 257,314
The GCF of 875,810 is 5 .
LCM of 257,314 is 80698.
The greatest common factor of 875/257,810/314 = [GCF of 875,810]/[LCM of 257,314]= 5/80698
Therefore, the GCF of 875/257,810/314 is 5/80698.
To find the highest common factor of 875,810, we have to find the factors of both numbers and list the highest common factor.
The factors of 875 are 1, 5, 7, 25, 35, 125, 175, 875
The factors of 810 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405, 810
The HCF of 875,810 is 5.
Lets's calculate GCF of 875,810
| 5 | 875, 810 |
| 175, 162 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 875,810 By Matching Biggest Common Factor Method
Now, list down the factors of 875
:1,5,7,25,35,125,175,875
Now, list down the factors of 810
:1,2,3,5,6,9,10,15,18,27,30,45,54,81,90,135,162,270,405,810
Greatest Common Factor
We found the factors 875,810 . The biggest common factor number is the GCF number.
So the greatest common factor 875,810 is 5.
Lets's calculate LCM of 257,314
Given numbers has no common factors except 1. So, there LCM is their product i.e 80698
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/80698
Therefore, the GCF of Fractions 875/257,810/314 is 5/80698
Least Common Multiple of 257,314 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 257,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(257,314) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(257,314) x common factors =1 x 1 = 1
LCM(257,314) = ( 257 × 314 ) / 1
LCM(257,314) = 80698 / 1
LCM(257,314) = 80698
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FAQs on GCF of Fractions of 875/257, 810/314
1. What is the HCF of 875,810?
The HCF of 875,810 is 5
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 875/257, 810/314?
Answer: GCF of Numerators as per given numbers 875/257, 810/314 is
GCF of Numerators i.e. for 875,810 is 5
LCM of denominators i.e. for 257,314 is 80698.
Thus, GCF of Fractions is 5/80698.Finally, GCF of Fractions for 875/257, 810/314 is 5/80698.