Use our free GCF of Fractions Calculator tool to compute the GCF of 49/942, 516/642, 384/214 i.e 1/100794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 49/942, 516/642, 384/214.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 49/942,516/642,384/214
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 49/942,516/642,384/214, numerators are 49,516,384
Denominators are 942,642,214
The GCF of 49,516,384 is 1 .
LCM of 942,642,214 is 100794.
The greatest common factor of 49/942,516/642,384/214 = [GCF of 49,516,384]/[LCM of 942,642,214]= 1/100794
Therefore, the GCF of 49/942,516/642,384/214 is 1/100794.
To find the highest common factor of 49,516,384, we have to find the factors of both numbers and list the highest common factor.
The factors of 49 are 1, 7, 49
The factors of 516 are 1, 2, 3, 4, 6, 12, 43, 86, 129, 172, 258, 516
The factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384
The HCF of 49,516,384 is 1.
Lets's calculate GCF of 49,516,384
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 49
:1,7,49
Now, list down the factors of 516
:1,2,3,4,6,12,43,86,129,172,258,516
Now, list down the factors of 384
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384
Greatest Common Factor
We found the factors 49,516,384 . The biggest common factor number is the GCF number.
So the greatest common factor 49,516,384 is 1.
Lets's calculate LCM of 942,642,214
2 | 942, 642, 214 |
3 | 471, 321, 107 |
107 | 157, 107, 107 |
157, 1, 1 |
∴ So the LCM of the given numbers is 2 x 3 x 107 x 157 x 1 x 1 = 100794
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/100794
Therefore, the GCF of Fractions 49/942,516/642,384/214 is 1/100794
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 942,642,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(942,642,214) = 2
common factors(in case of two or more numbers have common factors) = 642
GCF(942,642,214) x common factors =2 x 642 = 1284
LCM(942,642,214) = ( 942 × 642 × 214 ) / 1284
LCM(942,642,214) = 129419496 / 1284
LCM(942,642,214) = 100794
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 49,516,384?
The HCF of 49,516,384 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 49/942, 516/642, 384/214?
Answer: GCF of Numerators as per given numbers 49/942, 516/642, 384/214 is
GCF of Numerators i.e. for 49,516,384 is 1
LCM of denominators i.e. for 942,642,214 is 100794.
Thus, GCF of Fractions is 1/100794.Finally, GCF of Fractions for 49/942, 516/642, 384/214 is 1/100794.