Use our free GCF of Fractions Calculator tool to compute the GCF of 319/196, 424/348 i.e 1/17052 easily. The following is the detailed procedure to determine the greatest common factor of fractions 319/196, 424/348.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 319/196,424/348
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 319/196,424/348, numerators are 319,424
Denominators are 196,348
The GCF of 319,424 is 1 .
LCM of 196,348 is 17052.
The greatest common factor of 319/196,424/348 = [GCF of 319,424]/[LCM of 196,348]= 1/17052
Therefore, the GCF of 319/196,424/348 is 1/17052.
To find the highest common factor of 319,424, we have to find the factors of both numbers and list the highest common factor.
The factors of 319 are 1, 11, 29, 319
The factors of 424 are 1, 2, 4, 8, 53, 106, 212, 424
The HCF of 319,424 is 1.
Lets's calculate GCF of 319,424
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 319
:1,11,29,319
Now, list down the factors of 424
:1,2,4,8,53,106,212,424
Greatest Common Factor
We found the factors 319,424 . The biggest common factor number is the GCF number.
So the greatest common factor 319,424 is 1.
Lets's calculate LCM of 196,348
2 | 196, 348 |
2 | 98, 174 |
49, 87 |
∴ So the LCM of the given numbers is 2 x 2 x 49 x 87 = 17052
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17052
Therefore, the GCF of Fractions 319/196,424/348 is 1/17052
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 196,348 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(196,348) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(196,348) x common factors =4 x 1 = 4
LCM(196,348) = ( 196 × 348 ) / 4
LCM(196,348) = 68208 / 4
LCM(196,348) = 17052
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 319,424?
The HCF of 319,424 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 319/196, 424/348?
Answer: GCF of Numerators as per given numbers 319/196, 424/348 is
GCF of Numerators i.e. for 319,424 is 1
LCM of denominators i.e. for 196,348 is 17052.
Thus, GCF of Fractions is 1/17052.Finally, GCF of Fractions for 319/196, 424/348 is 1/17052.