Use our free GCF of Fractions Calculator tool to compute the GCF of 312/766, 510/740 i.e 6/283420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/766, 510/740.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 312/766,510/740
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 312/766,510/740, numerators are 312,510
Denominators are 766,740
The GCF of 312,510 is 6 .
LCM of 766,740 is 283420.
The greatest common factor of 312/766,510/740 = [GCF of 312,510]/[LCM of 766,740]= 6/283420
Therefore, the GCF of 312/766,510/740 is 6/283420.
To find the highest common factor of 312,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 312,510 is 6.
Lets's calculate GCF of 312,510
2 | 312, 510 |
3 | 156, 255 |
52, 85 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Greatest Common Factor
We found the factors 312,510 . The biggest common factor number is the GCF number.
So the greatest common factor 312,510 is 6.
Lets's calculate LCM of 766,740
2 | 766, 740 |
383, 370 |
∴ So the LCM of the given numbers is 2 x 383 x 370 = 283420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/283420
Therefore, the GCF of Fractions 312/766,510/740 is 6/283420
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 766,740 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(766,740) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(766,740) x common factors =2 x 1 = 2
LCM(766,740) = ( 766 × 740 ) / 2
LCM(766,740) = 566840 / 2
LCM(766,740) = 283420
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 312,510?
The HCF of 312,510 is 6
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 312/766, 510/740?
Answer: GCF of Numerators as per given numbers 312/766, 510/740 is
GCF of Numerators i.e. for 312,510 is 6
LCM of denominators i.e. for 766,740 is 283420.
Thus, GCF of Fractions is 6/283420.Finally, GCF of Fractions for 312/766, 510/740 is 6/283420.