Use our free GCF of Fractions Calculator tool to compute the GCF of 199/107, 280/315 i.e 1/33705 easily. The following is the detailed procedure to determine the greatest common factor of fractions 199/107, 280/315.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 199/107,280/315
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 199/107,280/315, numerators are 199,280
Denominators are 107,315
The GCF of 199,280 is 1 .
LCM of 107,315 is 33705.
The greatest common factor of 199/107,280/315 = [GCF of 199,280]/[LCM of 107,315]= 1/33705
Therefore, the GCF of 199/107,280/315 is 1/33705.
To find the highest common factor of 199,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 199 are 1, 199
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 199,280 is 1.
Lets's calculate GCF of 199,280
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 199
:1,199
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 199,280 . The biggest common factor number is the GCF number.
So the greatest common factor 199,280 is 1.
Lets's calculate LCM of 107,315
Given numbers has no common factors except 1. So, there LCM is their product i.e 33705
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/33705
Therefore, the GCF of Fractions 199/107,280/315 is 1/33705
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 107,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(107,315) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(107,315) x common factors =1 x 1 = 1
LCM(107,315) = ( 107 × 315 ) / 1
LCM(107,315) = 33705 / 1
LCM(107,315) = 33705
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 199,280?
The HCF of 199,280 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 199/107, 280/315?
Answer: GCF of Numerators as per given numbers 199/107, 280/315 is
GCF of Numerators i.e. for 199,280 is 1
LCM of denominators i.e. for 107,315 is 33705.
Thus, GCF of Fractions is 1/33705.Finally, GCF of Fractions for 199/107, 280/315 is 1/33705.