GCF of 110/431, 8270/1214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 110/431, 8270/1214 i.e 10/523234 easily. The following is the detailed procedure to determine the greatest common factor of fractions 110/431, 8270/1214.
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 110/431,8270/1214?
Given fractions are 110/431,8270/1214
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 110/431,8270/1214, numerators are 110,8270
Denominators are 431,1214
The GCF of 110,8270 is 10 .
LCM of 431,1214 is 523234.
The greatest common factor of 110/431,8270/1214 = [GCF of 110,8270]/[LCM of 431,1214]= 10/523234
Therefore, the GCF of 110/431,8270/1214 is 10/523234.
To find the highest common factor of 110,8270, we have to find the factors of both numbers and list the highest common factor.
The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110
The factors of 8270 are 1, 2, 5, 10, 827, 1654, 4135, 8270
The HCF of 110,8270 is 10.
Lets's calculate GCF of 110,8270
| 2 | 110, 8270 |
| 5 | 55, 4135 |
| 11, 827 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 110,8270 By Matching Biggest Common Factor Method
Now, list down the factors of 110
:1,2,5,10,11,22,55,110
Now, list down the factors of 8270
:1,2,5,10,827,1654,4135,8270
Greatest Common Factor
We found the factors 110,8270 . The biggest common factor number is the GCF number.
So the greatest common factor 110,8270 is 10.
Lets's calculate LCM of 431,1214
Given numbers has no common factors except 1. So, there LCM is their product i.e 523234
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/523234
Therefore, the GCF of Fractions 110/431,8270/1214 is 10/523234
Least Common Multiple of 431,1214 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 431,1214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(431,1214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(431,1214) x common factors =1 x 1 = 1
LCM(431,1214) = ( 431 × 1214 ) / 1
LCM(431,1214) = 523234 / 1
LCM(431,1214) = 523234
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 110/431, 8270/1214
1. What is the HCF of 110,8270?
The HCF of 110,8270 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 110/431, 8270/1214?
Answer: GCF of Numerators as per given numbers 110/431, 8270/1214 is
GCF of Numerators i.e. for 110,8270 is 10
LCM of denominators i.e. for 431,1214 is 523234.
Thus, GCF of Fractions is 10/523234.Finally, GCF of Fractions for 110/431, 8270/1214 is 10/523234.