Use our free GCF of Fractions Calculator tool to compute the GCF of 382/821, 6816/175 i.e 2/143675 easily. The following is the detailed procedure to determine the greatest common factor of fractions 382/821, 6816/175.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 382/821,6816/175
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 382/821,6816/175, numerators are 382,6816
Denominators are 821,175
The GCF of 382,6816 is 2 .
LCM of 821,175 is 143675.
The greatest common factor of 382/821,6816/175 = [GCF of 382,6816]/[LCM of 821,175]= 2/143675
Therefore, the GCF of 382/821,6816/175 is 2/143675.
To find the highest common factor of 382,6816, we have to find the factors of both numbers and list the highest common factor.
The factors of 382 are 1, 2, 191, 382
The factors of 6816 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 71, 96, 142, 213, 284, 426, 568, 852, 1136, 1704, 2272, 3408, 6816
The HCF of 382,6816 is 2.
Lets's calculate GCF of 382,6816
2 | 382, 6816 |
191, 3408 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 382
:1,2,191,382
Now, list down the factors of 6816
:1,2,3,4,6,8,12,16,24,32,48,71,96,142,213,284,426,568,852,1136,1704,2272,3408,6816
Greatest Common Factor
We found the factors 382,6816 . The biggest common factor number is the GCF number.
So the greatest common factor 382,6816 is 2.
Lets's calculate LCM of 821,175
Given numbers has no common factors except 1. So, there LCM is their product i.e 143675
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/143675
Therefore, the GCF of Fractions 382/821,6816/175 is 2/143675
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 821,175 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(821,175) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(821,175) x common factors =1 x 1 = 1
LCM(821,175) = ( 821 × 175 ) / 1
LCM(821,175) = 143675 / 1
LCM(821,175) = 143675
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 382,6816?
The HCF of 382,6816 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 382/821, 6816/175?
Answer: GCF of Numerators as per given numbers 382/821, 6816/175 is
GCF of Numerators i.e. for 382,6816 is 2
LCM of denominators i.e. for 821,175 is 143675.
Thus, GCF of Fractions is 2/143675.Finally, GCF of Fractions for 382/821, 6816/175 is 2/143675.