Use our free GCF of Fractions Calculator tool to compute the GCF of 816/778, 612/803 i.e 204/624734 easily. The following is the detailed procedure to determine the greatest common factor of fractions 816/778, 612/803.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 816/778,612/803
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 816/778,612/803, numerators are 816,612
Denominators are 778,803
The GCF of 816,612 is 204 .
LCM of 778,803 is 624734.
The greatest common factor of 816/778,612/803 = [GCF of 816,612]/[LCM of 778,803]= 204/624734
Therefore, the GCF of 816/778,612/803 is 204/624734.
To find the highest common factor of 816,612, we have to find the factors of both numbers and list the highest common factor.
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 factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The HCF of 816,612 is 204.
Lets's calculate GCF of 816,612
2 | 816, 612 |
2 | 408, 306 |
3 | 204, 153 |
17 | 68, 51 |
4, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 17 = 204
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
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Greatest Common Factor
We found the factors 816,612 . The biggest common factor number is the GCF number.
So the greatest common factor 816,612 is 204.
Lets's calculate LCM of 778,803
Given numbers has no common factors except 1. So, there LCM is their product i.e 624734
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 204/624734
Therefore, the GCF of Fractions 816/778,612/803 is 204/624734
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 778,803 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(778,803) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(778,803) x common factors =1 x 1 = 1
LCM(778,803) = ( 778 × 803 ) / 1
LCM(778,803) = 624734 / 1
LCM(778,803) = 624734
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 816,612?
The HCF of 816,612 is 204
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 816/778, 612/803?
Answer: GCF of Numerators as per given numbers 816/778, 612/803 is
GCF of Numerators i.e. for 816,612 is 204
LCM of denominators i.e. for 778,803 is 624734.
Thus, GCF of Fractions is 204/624734.Finally, GCF of Fractions for 816/778, 612/803 is 204/624734.