Use our free GCF of Fractions Calculator tool to compute the GCF of 57/69, 219/74, 214/355 i.e 1/1812630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 57/69, 219/74, 214/355.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 57/69,219/74,214/355
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 57/69,219/74,214/355, numerators are 57,219,214
Denominators are 69,74,355
The GCF of 57,219,214 is 1 .
LCM of 69,74,355 is 1812630.
The greatest common factor of 57/69,219/74,214/355 = [GCF of 57,219,214]/[LCM of 69,74,355]= 1/1812630
Therefore, the GCF of 57/69,219/74,214/355 is 1/1812630.
To find the highest common factor of 57,219,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 57 are 1, 3, 19, 57
The factors of 219 are 1, 3, 73, 219
The factors of 214 are 1, 2, 107, 214
The HCF of 57,219,214 is 1.
Lets's calculate GCF of 57,219,214
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 57
:1,3,19,57
Now, list down the factors of 219
:1,3,73,219
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 57,219,214 . The biggest common factor number is the GCF number.
So the greatest common factor 57,219,214 is 1.
Lets's calculate LCM of 69,74,355
Given numbers has no common factors except 1. So, there LCM is their product i.e 1812630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1812630
Therefore, the GCF of Fractions 57/69,219/74,214/355 is 1/1812630
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 69,74,355 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,74,355) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(69,74,355) x common factors =1 x 1 = 1
LCM(69,74,355) = ( 69 × 74 × 355 ) / 1
LCM(69,74,355) = 1812630 / 1
LCM(69,74,355) = 1812630
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 57,219,214?
The HCF of 57,219,214 is 1
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 57/69, 219/74, 214/355?
Answer: GCF of Numerators as per given numbers 57/69, 219/74, 214/355 is
GCF of Numerators i.e. for 57,219,214 is 1
LCM of denominators i.e. for 69,74,355 is 1812630.
Thus, GCF of Fractions is 1/1812630.Finally, GCF of Fractions for 57/69, 219/74, 214/355 is 1/1812630.