Use our free GCF of Fractions Calculator tool to compute the GCF of 785/749, 510/229 i.e 5/171521 easily. The following is the detailed procedure to determine the greatest common factor of fractions 785/749, 510/229.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 785/749,510/229
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 785/749,510/229, numerators are 785,510
Denominators are 749,229
The GCF of 785,510 is 5 .
LCM of 749,229 is 171521.
The greatest common factor of 785/749,510/229 = [GCF of 785,510]/[LCM of 749,229]= 5/171521
Therefore, the GCF of 785/749,510/229 is 5/171521.
To find the highest common factor of 785,510, we have to find the factors of both numbers and list the highest common factor.
The factors of 785 are 1, 5, 157, 785
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The HCF of 785,510 is 5.
Lets's calculate GCF of 785,510
5 | 785, 510 |
157, 102 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 785
:1,5,157,785
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 785,510 . The biggest common factor number is the GCF number.
So the greatest common factor 785,510 is 5.
Lets's calculate LCM of 749,229
Given numbers has no common factors except 1. So, there LCM is their product i.e 171521
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/171521
Therefore, the GCF of Fractions 785/749,510/229 is 5/171521
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 749,229 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(749,229) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(749,229) x common factors =1 x 1 = 1
LCM(749,229) = ( 749 × 229 ) / 1
LCM(749,229) = 171521 / 1
LCM(749,229) = 171521
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 785,510?
The HCF of 785,510 is 5
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 785/749, 510/229?
Answer: GCF of Numerators as per given numbers 785/749, 510/229 is
GCF of Numerators i.e. for 785,510 is 5
LCM of denominators i.e. for 749,229 is 171521.
Thus, GCF of Fractions is 5/171521.Finally, GCF of Fractions for 785/749, 510/229 is 5/171521.