GCF of 250/422, 320/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 250/422, 320/214 i.e 10/45154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 250/422, 320/214.
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 250/422,320/214?
Given fractions are 250/422,320/214
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 250/422,320/214, numerators are 250,320
Denominators are 422,214
The GCF of 250,320 is 10 .
LCM of 422,214 is 45154.
The greatest common factor of 250/422,320/214 = [GCF of 250,320]/[LCM of 422,214]= 10/45154
Therefore, the GCF of 250/422,320/214 is 10/45154.
To find the highest common factor of 250,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 250 are 1, 2, 5, 10, 25, 50, 125, 250
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 250,320 is 10.
Lets's calculate GCF of 250,320
| 2 | 250, 320 |
| 5 | 125, 160 |
| 25, 32 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 250,320 By Matching Biggest Common Factor Method
Now, list down the factors of 250
:1,2,5,10,25,50,125,250
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 250,320 . The biggest common factor number is the GCF number.
So the greatest common factor 250,320 is 10.
Lets's calculate LCM of 422,214
| 2 | 422, 214 |
| 211, 107 |
∴ So the LCM of the given numbers is 2 x 211 x 107 = 45154
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/45154
Therefore, the GCF of Fractions 250/422,320/214 is 10/45154
Least Common Multiple of 422,214 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 422,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(422,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(422,214) x common factors =2 x 1 = 2
LCM(422,214) = ( 422 × 214 ) / 2
LCM(422,214) = 90308 / 2
LCM(422,214) = 45154
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 250/422, 320/214
1. What is the HCF of 250,320?
The HCF of 250,320 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 250/422, 320/214?
Answer: GCF of Numerators as per given numbers 250/422, 320/214 is
GCF of Numerators i.e. for 250,320 is 10
LCM of denominators i.e. for 422,214 is 45154.
Thus, GCF of Fractions is 10/45154.Finally, GCF of Fractions for 250/422, 320/214 is 10/45154.