Use our free GCF of Fractions Calculator tool to compute the GCF of 378/523, 336/773 i.e 42/404279 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/523, 336/773.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 378/523,336/773
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 378/523,336/773, numerators are 378,336
Denominators are 523,773
The GCF of 378,336 is 42 .
LCM of 523,773 is 404279.
The greatest common factor of 378/523,336/773 = [GCF of 378,336]/[LCM of 523,773]= 42/404279
Therefore, the GCF of 378/523,336/773 is 42/404279.
To find the highest common factor of 378,336, we have to find the factors of both numbers and list the highest common factor.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336
The HCF of 378,336 is 42.
Lets's calculate GCF of 378,336
2 | 378, 336 |
3 | 189, 168 |
7 | 63, 56 |
9, 8 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 336
:1,2,3,4,6,7,8,12,14,16,21,24,28,42,48,56,84,112,168,336
Greatest Common Factor
We found the factors 378,336 . The biggest common factor number is the GCF number.
So the greatest common factor 378,336 is 42.
Lets's calculate LCM of 523,773
Given numbers has no common factors except 1. So, there LCM is their product i.e 404279
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/404279
Therefore, the GCF of Fractions 378/523,336/773 is 42/404279
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 523,773 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(523,773) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(523,773) x common factors =1 x 1 = 1
LCM(523,773) = ( 523 × 773 ) / 1
LCM(523,773) = 404279 / 1
LCM(523,773) = 404279
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 378,336?
The HCF of 378,336 is 42
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 378/523, 336/773?
Answer: GCF of Numerators as per given numbers 378/523, 336/773 is
GCF of Numerators i.e. for 378,336 is 42
LCM of denominators i.e. for 523,773 is 404279.
Thus, GCF of Fractions is 42/404279.Finally, GCF of Fractions for 378/523, 336/773 is 42/404279.