Use our free GCF of Fractions Calculator tool to compute the GCF of 702/828, 398/213 i.e 2/58788 easily. The following is the detailed procedure to determine the greatest common factor of fractions 702/828, 398/213.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 702/828,398/213
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 702/828,398/213, numerators are 702,398
Denominators are 828,213
The GCF of 702,398 is 2 .
LCM of 828,213 is 58788.
The greatest common factor of 702/828,398/213 = [GCF of 702,398]/[LCM of 828,213]= 2/58788
Therefore, the GCF of 702/828,398/213 is 2/58788.
To find the highest common factor of 702,398, we have to find the factors of both numbers and list the highest common factor.
The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
The factors of 398 are 1, 2, 199, 398
The HCF of 702,398 is 2.
Lets's calculate GCF of 702,398
2 | 702, 398 |
351, 199 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 702
:1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Now, list down the factors of 398
:1,2,199,398
Greatest Common Factor
We found the factors 702,398 . The biggest common factor number is the GCF number.
So the greatest common factor 702,398 is 2.
Lets's calculate LCM of 828,213
3 | 828, 213 |
276, 71 |
∴ So the LCM of the given numbers is 3 x 276 x 71 = 58788
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/58788
Therefore, the GCF of Fractions 702/828,398/213 is 2/58788
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 828,213 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(828,213) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(828,213) x common factors =3 x 1 = 3
LCM(828,213) = ( 828 × 213 ) / 3
LCM(828,213) = 176364 / 3
LCM(828,213) = 58788
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 702,398?
The HCF of 702,398 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 702/828, 398/213?
Answer: GCF of Numerators as per given numbers 702/828, 398/213 is
GCF of Numerators i.e. for 702,398 is 2
LCM of denominators i.e. for 828,213 is 58788.
Thus, GCF of Fractions is 2/58788.Finally, GCF of Fractions for 702/828, 398/213 is 2/58788.