Use our free GCF of Fractions Calculator tool to compute the GCF of 504/756, 354/380 i.e 6/71820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 504/756, 354/380.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 504/756,354/380
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 504/756,354/380, numerators are 504,354
Denominators are 756,380
The GCF of 504,354 is 6 .
LCM of 756,380 is 71820.
The greatest common factor of 504/756,354/380 = [GCF of 504,354]/[LCM of 756,380]= 6/71820
Therefore, the GCF of 504/756,354/380 is 6/71820.
To find the highest common factor of 504,354, we have to find the factors of both numbers and list the highest common factor.
The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
The factors of 354 are 1, 2, 3, 6, 59, 118, 177, 354
The HCF of 504,354 is 6.
Lets's calculate GCF of 504,354
2 | 504, 354 |
3 | 252, 177 |
84, 59 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 504
:1,2,3,4,6,7,8,9,12,14,18,21,24,28,36,42,56,63,72,84,126,168,252,504
Now, list down the factors of 354
:1,2,3,6,59,118,177,354
Greatest Common Factor
We found the factors 504,354 . The biggest common factor number is the GCF number.
So the greatest common factor 504,354 is 6.
Lets's calculate LCM of 756,380
2 | 756, 380 |
2 | 378, 190 |
189, 95 |
∴ So the LCM of the given numbers is 2 x 2 x 189 x 95 = 71820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/71820
Therefore, the GCF of Fractions 504/756,354/380 is 6/71820
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 756,380 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,380) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(756,380) x common factors =4 x 1 = 4
LCM(756,380) = ( 756 × 380 ) / 4
LCM(756,380) = 287280 / 4
LCM(756,380) = 71820
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 504,354?
The HCF of 504,354 is 6
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 504/756, 354/380?
Answer: GCF of Numerators as per given numbers 504/756, 354/380 is
GCF of Numerators i.e. for 504,354 is 6
LCM of denominators i.e. for 756,380 is 71820.
Thus, GCF of Fractions is 6/71820.Finally, GCF of Fractions for 504/756, 354/380 is 6/71820.