GCF of 860/64, 310/8174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 860/64, 310/8174 i.e 10/261568 easily. The following is the detailed procedure to determine the greatest common factor of fractions 860/64, 310/8174.
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 860/64,310/8174?
Given fractions are 860/64,310/8174
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 860/64,310/8174, numerators are 860,310
Denominators are 64,8174
The GCF of 860,310 is 10 .
LCM of 64,8174 is 261568.
The greatest common factor of 860/64,310/8174 = [GCF of 860,310]/[LCM of 64,8174]= 10/261568
Therefore, the GCF of 860/64,310/8174 is 10/261568.
To find the highest common factor of 860,310, we have to find the factors of both numbers and list the highest common factor.
The factors of 860 are 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The HCF of 860,310 is 10.
Lets's calculate GCF of 860,310
| 2 | 860, 310 |
| 5 | 430, 155 |
| 86, 31 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 860,310 By Matching Biggest Common Factor Method
Now, list down the factors of 860
:1,2,4,5,10,20,43,86,172,215,430,860
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Greatest Common Factor
We found the factors 860,310 . The biggest common factor number is the GCF number.
So the greatest common factor 860,310 is 10.
Lets's calculate LCM of 64,8174
| 2 | 64, 8174 |
| 32, 4087 |
∴ So the LCM of the given numbers is 2 x 32 x 4087 = 261568
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/261568
Therefore, the GCF of Fractions 860/64,310/8174 is 10/261568
Least Common Multiple of 64,8174 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 64,8174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,8174) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(64,8174) x common factors =2 x 1 = 2
LCM(64,8174) = ( 64 × 8174 ) / 2
LCM(64,8174) = 523136 / 2
LCM(64,8174) = 261568
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 860/64, 310/8174
1. What is the HCF of 860,310?
The HCF of 860,310 is 10
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 860/64, 310/8174?
Answer: GCF of Numerators as per given numbers 860/64, 310/8174 is
GCF of Numerators i.e. for 860,310 is 10
LCM of denominators i.e. for 64,8174 is 261568.
Thus, GCF of Fractions is 10/261568.Finally, GCF of Fractions for 860/64, 310/8174 is 10/261568.