Use our free GCF of Fractions Calculator tool to compute the GCF of 294/731, 210/538 i.e 42/393278 easily. The following is the detailed procedure to determine the greatest common factor of fractions 294/731, 210/538.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 294/731,210/538
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 294/731,210/538, numerators are 294,210
Denominators are 731,538
The GCF of 294,210 is 42 .
LCM of 731,538 is 393278.
The greatest common factor of 294/731,210/538 = [GCF of 294,210]/[LCM of 731,538]= 42/393278
Therefore, the GCF of 294/731,210/538 is 42/393278.
To find the highest common factor of 294,210, we have to find the factors of both numbers and list the highest common factor.
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
The HCF of 294,210 is 42.
Lets's calculate GCF of 294,210
2 | 294, 210 |
3 | 147, 105 |
7 | 49, 35 |
7, 5 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Now, list down the factors of 210
:1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210
Greatest Common Factor
We found the factors 294,210 . The biggest common factor number is the GCF number.
So the greatest common factor 294,210 is 42.
Lets's calculate LCM of 731,538
Given numbers has no common factors except 1. So, there LCM is their product i.e 393278
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/393278
Therefore, the GCF of Fractions 294/731,210/538 is 42/393278
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 731,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(731,538) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(731,538) x common factors =1 x 1 = 1
LCM(731,538) = ( 731 × 538 ) / 1
LCM(731,538) = 393278 / 1
LCM(731,538) = 393278
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 294,210?
The HCF of 294,210 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 294/731, 210/538?
Answer: GCF of Numerators as per given numbers 294/731, 210/538 is
GCF of Numerators i.e. for 294,210 is 42
LCM of denominators i.e. for 731,538 is 393278.
Thus, GCF of Fractions is 42/393278.Finally, GCF of Fractions for 294/731, 210/538 is 42/393278.