Use our free GCF of Fractions Calculator tool to compute the GCF of 30/818, 42/280, 506/612 i.e 2/17521560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/818, 42/280, 506/612.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/818,42/280,506/612
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 30/818,42/280,506/612, numerators are 30,42,506
Denominators are 818,280,612
The GCF of 30,42,506 is 2 .
LCM of 818,280,612 is 17521560.
The greatest common factor of 30/818,42/280,506/612 = [GCF of 30,42,506]/[LCM of 818,280,612]= 2/17521560
Therefore, the GCF of 30/818,42/280,506/612 is 2/17521560.
To find the highest common factor of 30,42,506, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The HCF of 30,42,506 is 2.
Lets's calculate GCF of 30,42,506
2 | 30, 42, 506 |
15, 21, 253 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Greatest Common Factor
We found the factors 30,42,506 . The biggest common factor number is the GCF number.
So the greatest common factor 30,42,506 is 2.
Lets's calculate LCM of 818,280,612
2 | 818, 280, 612 |
2 | 409, 140, 306 |
409, 70, 153 |
∴ So the LCM of the given numbers is 2 x 2 x 409 x 70 x 153 = 17521560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/17521560
Therefore, the GCF of Fractions 30/818,42/280,506/612 is 2/17521560
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 818,280,612 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(818,280,612) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(818,280,612) x common factors =2 x 4 = 8
LCM(818,280,612) = ( 818 × 280 × 612 ) / 8
LCM(818,280,612) = 140172480 / 8
LCM(818,280,612) = 17521560
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,42,506?
The HCF of 30,42,506 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 30/818, 42/280, 506/612?
Answer: GCF of Numerators as per given numbers 30/818, 42/280, 506/612 is
GCF of Numerators i.e. for 30,42,506 is 2
LCM of denominators i.e. for 818,280,612 is 17521560.
Thus, GCF of Fractions is 2/17521560.Finally, GCF of Fractions for 30/818, 42/280, 506/612 is 2/17521560.