Use our free GCF of Fractions Calculator tool to compute the GCF of 429/678, 816/306 i.e 3/34578 easily. The following is the detailed procedure to determine the greatest common factor of fractions 429/678, 816/306.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 429/678,816/306
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 429/678,816/306, numerators are 429,816
Denominators are 678,306
The GCF of 429,816 is 3 .
LCM of 678,306 is 34578.
The greatest common factor of 429/678,816/306 = [GCF of 429,816]/[LCM of 678,306]= 3/34578
Therefore, the GCF of 429/678,816/306 is 3/34578.
To find the highest common factor of 429,816, we have to find the factors of both numbers and list the highest common factor.
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The factors of 816 are 1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 68, 102, 136, 204, 272, 408, 816
The HCF of 429,816 is 3.
Lets's calculate GCF of 429,816
3 | 429, 816 |
143, 272 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Now, list down the factors of 816
:1,2,3,4,6,8,12,16,17,24,34,48,51,68,102,136,204,272,408,816
Greatest Common Factor
We found the factors 429,816 . The biggest common factor number is the GCF number.
So the greatest common factor 429,816 is 3.
Lets's calculate LCM of 678,306
2 | 678, 306 |
3 | 339, 153 |
113, 51 |
∴ So the LCM of the given numbers is 2 x 3 x 113 x 51 = 34578
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/34578
Therefore, the GCF of Fractions 429/678,816/306 is 3/34578
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 678,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,306) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(678,306) x common factors =6 x 1 = 6
LCM(678,306) = ( 678 × 306 ) / 6
LCM(678,306) = 207468 / 6
LCM(678,306) = 34578
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 429,816?
The HCF of 429,816 is 3
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 429/678, 816/306?
Answer: GCF of Numerators as per given numbers 429/678, 816/306 is
GCF of Numerators i.e. for 429,816 is 3
LCM of denominators i.e. for 678,306 is 34578.
Thus, GCF of Fractions is 3/34578.Finally, GCF of Fractions for 429/678, 816/306 is 3/34578.