Use our free GCF of Fractions Calculator tool to compute the GCF of 371/704, 378/924 i.e 7/14784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 371/704, 378/924.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 371/704,378/924
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 371/704,378/924, numerators are 371,378
Denominators are 704,924
The GCF of 371,378 is 7 .
LCM of 704,924 is 14784.
The greatest common factor of 371/704,378/924 = [GCF of 371,378]/[LCM of 704,924]= 7/14784
Therefore, the GCF of 371/704,378/924 is 7/14784.
To find the highest common factor of 371,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 371 are 1, 7, 53, 371
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 371,378 is 7.
Lets's calculate GCF of 371,378
7 | 371, 378 |
53, 54 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 371
:1,7,53,371
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 371,378 . The biggest common factor number is the GCF number.
So the greatest common factor 371,378 is 7.
Lets's calculate LCM of 704,924
2 | 704, 924 |
2 | 352, 462 |
11 | 176, 231 |
16, 21 |
∴ So the LCM of the given numbers is 2 x 2 x 11 x 16 x 21 = 14784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/14784
Therefore, the GCF of Fractions 371/704,378/924 is 7/14784
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 704,924 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(704,924) = 44
common factors(in case of two or more numbers have common factors) = 1
GCF(704,924) x common factors =44 x 1 = 44
LCM(704,924) = ( 704 × 924 ) / 44
LCM(704,924) = 650496 / 44
LCM(704,924) = 14784
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 371,378?
The HCF of 371,378 is 7
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 371/704, 378/924?
Answer: GCF of Numerators as per given numbers 371/704, 378/924 is
GCF of Numerators i.e. for 371,378 is 7
LCM of denominators i.e. for 704,924 is 14784.
Thus, GCF of Fractions is 7/14784.Finally, GCF of Fractions for 371/704, 378/924 is 7/14784.