Use our free GCF of Fractions Calculator tool to compute the GCF of 386/645, 312/294 i.e 2/63210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 386/645, 312/294.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 386/645,312/294
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 386/645,312/294, numerators are 386,312
Denominators are 645,294
The GCF of 386,312 is 2 .
LCM of 645,294 is 63210.
The greatest common factor of 386/645,312/294 = [GCF of 386,312]/[LCM of 645,294]= 2/63210
Therefore, the GCF of 386/645,312/294 is 2/63210.
To find the highest common factor of 386,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 386 are 1, 2, 193, 386
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 386,312 is 2.
Lets's calculate GCF of 386,312
2 | 386, 312 |
193, 156 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 386
:1,2,193,386
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 386,312 . The biggest common factor number is the GCF number.
So the greatest common factor 386,312 is 2.
Lets's calculate LCM of 645,294
3 | 645, 294 |
215, 98 |
∴ So the LCM of the given numbers is 3 x 215 x 98 = 63210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/63210
Therefore, the GCF of Fractions 386/645,312/294 is 2/63210
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 645,294 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(645,294) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(645,294) x common factors =3 x 1 = 3
LCM(645,294) = ( 645 × 294 ) / 3
LCM(645,294) = 189630 / 3
LCM(645,294) = 63210
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 386,312?
The HCF of 386,312 is 2
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 386/645, 312/294?
Answer: GCF of Numerators as per given numbers 386/645, 312/294 is
GCF of Numerators i.e. for 386,312 is 2
LCM of denominators i.e. for 645,294 is 63210.
Thus, GCF of Fractions is 2/63210.Finally, GCF of Fractions for 386/645, 312/294 is 2/63210.