Use our free GCF of Fractions Calculator tool to compute the GCF of 322/691, 542/278 i.e 2/192098 easily. The following is the detailed procedure to determine the greatest common factor of fractions 322/691, 542/278.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 322/691,542/278
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 322/691,542/278, numerators are 322,542
Denominators are 691,278
The GCF of 322,542 is 2 .
LCM of 691,278 is 192098.
The greatest common factor of 322/691,542/278 = [GCF of 322,542]/[LCM of 691,278]= 2/192098
Therefore, the GCF of 322/691,542/278 is 2/192098.
To find the highest common factor of 322,542, we have to find the factors of both numbers and list the highest common factor.
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The factors of 542 are 1, 2, 271, 542
The HCF of 322,542 is 2.
Lets's calculate GCF of 322,542
2 | 322, 542 |
161, 271 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Now, list down the factors of 542
:1,2,271,542
Greatest Common Factor
We found the factors 322,542 . The biggest common factor number is the GCF number.
So the greatest common factor 322,542 is 2.
Lets's calculate LCM of 691,278
Given numbers has no common factors except 1. So, there LCM is their product i.e 192098
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/192098
Therefore, the GCF of Fractions 322/691,542/278 is 2/192098
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 691,278 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(691,278) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(691,278) x common factors =1 x 1 = 1
LCM(691,278) = ( 691 × 278 ) / 1
LCM(691,278) = 192098 / 1
LCM(691,278) = 192098
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 322,542?
The HCF of 322,542 is 2
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 322/691, 542/278?
Answer: GCF of Numerators as per given numbers 322/691, 542/278 is
GCF of Numerators i.e. for 322,542 is 2
LCM of denominators i.e. for 691,278 is 192098.
Thus, GCF of Fractions is 2/192098.Finally, GCF of Fractions for 322/691, 542/278 is 2/192098.