Use our free GCF of Fractions Calculator tool to compute the GCF of 3662/816, 9649/1428 i.e 1/5712 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3662/816, 9649/1428.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 3662/816,9649/1428
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 3662/816,9649/1428, numerators are 3662,9649
Denominators are 816,1428
The GCF of 3662,9649 is 1 .
LCM of 816,1428 is 5712.
The greatest common factor of 3662/816,9649/1428 = [GCF of 3662,9649]/[LCM of 816,1428]= 1/5712
Therefore, the GCF of 3662/816,9649/1428 is 1/5712.
To find the highest common factor of 3662,9649, we have to find the factors of both numbers and list the highest common factor.
The factors of 3662 are 1, 2, 1831, 3662
The factors of 9649 are 1, 9649
The HCF of 3662,9649 is 1.
Lets's calculate GCF of 3662,9649
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 3662
:1,2,1831,3662
Now, list down the factors of 9649
:1,9649
Greatest Common Factor
We found the factors 3662,9649 . The biggest common factor number is the GCF number.
So the greatest common factor 3662,9649 is 1.
Lets's calculate LCM of 816,1428
2 | 816, 1428 |
2 | 408, 714 |
3 | 204, 357 |
17 | 68, 119 |
4, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 17 x 4 x 7 = 5712
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5712
Therefore, the GCF of Fractions 3662/816,9649/1428 is 1/5712
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 816,1428 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(816,1428) = 204
common factors(in case of two or more numbers have common factors) = 1
GCF(816,1428) x common factors =204 x 1 = 204
LCM(816,1428) = ( 816 × 1428 ) / 204
LCM(816,1428) = 1165248 / 204
LCM(816,1428) = 5712
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 3662,9649?
The HCF of 3662,9649 is 1
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 3662/816, 9649/1428?
Answer: GCF of Numerators as per given numbers 3662/816, 9649/1428 is
GCF of Numerators i.e. for 3662,9649 is 1
LCM of denominators i.e. for 816,1428 is 5712.
Thus, GCF of Fractions is 1/5712.Finally, GCF of Fractions for 3662/816, 9649/1428 is 1/5712.