Use our free GCF of Fractions Calculator tool to compute the GCF of 191/160, 294/420 i.e 1/3360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 191/160, 294/420.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 191/160,294/420
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 191/160,294/420, numerators are 191,294
Denominators are 160,420
The GCF of 191,294 is 1 .
LCM of 160,420 is 3360.
The greatest common factor of 191/160,294/420 = [GCF of 191,294]/[LCM of 160,420]= 1/3360
Therefore, the GCF of 191/160,294/420 is 1/3360.
To find the highest common factor of 191,294, we have to find the factors of both numbers and list the highest common factor.
The factors of 191 are 1, 191
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The HCF of 191,294 is 1.
Lets's calculate GCF of 191,294
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 191
:1,191
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 191,294 . The biggest common factor number is the GCF number.
So the greatest common factor 191,294 is 1.
Lets's calculate LCM of 160,420
2 | 160, 420 |
2 | 80, 210 |
5 | 40, 105 |
8, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 8 x 21 = 3360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3360
Therefore, the GCF of Fractions 191/160,294/420 is 1/3360
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 160,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(160,420) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(160,420) x common factors =20 x 1 = 20
LCM(160,420) = ( 160 × 420 ) / 20
LCM(160,420) = 67200 / 20
LCM(160,420) = 3360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 191,294?
The HCF of 191,294 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 191/160, 294/420?
Answer: GCF of Numerators as per given numbers 191/160, 294/420 is
GCF of Numerators i.e. for 191,294 is 1
LCM of denominators i.e. for 160,420 is 3360.
Thus, GCF of Fractions is 1/3360.Finally, GCF of Fractions for 191/160, 294/420 is 1/3360.