Use our free GCF of Fractions Calculator tool to compute the GCF of 175/354, 222/784 i.e 1/138768 easily. The following is the detailed procedure to determine the greatest common factor of fractions 175/354, 222/784.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 175/354,222/784
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 175/354,222/784, numerators are 175,222
Denominators are 354,784
The GCF of 175,222 is 1 .
LCM of 354,784 is 138768.
The greatest common factor of 175/354,222/784 = [GCF of 175,222]/[LCM of 354,784]= 1/138768
Therefore, the GCF of 175/354,222/784 is 1/138768.
To find the highest common factor of 175,222, we have to find the factors of both numbers and list the highest common factor.
The factors of 175 are 1, 5, 7, 25, 35, 175
The factors of 222 are 1, 2, 3, 6, 37, 74, 111, 222
The HCF of 175,222 is 1.
Lets's calculate GCF of 175,222
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 175
:1,5,7,25,35,175
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Greatest Common Factor
We found the factors 175,222 . The biggest common factor number is the GCF number.
So the greatest common factor 175,222 is 1.
Lets's calculate LCM of 354,784
2 | 354, 784 |
177, 392 |
∴ So the LCM of the given numbers is 2 x 177 x 392 = 138768
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/138768
Therefore, the GCF of Fractions 175/354,222/784 is 1/138768
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 354,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,784) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(354,784) x common factors =2 x 1 = 2
LCM(354,784) = ( 354 × 784 ) / 2
LCM(354,784) = 277536 / 2
LCM(354,784) = 138768
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 175,222?
The HCF of 175,222 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 175/354, 222/784?
Answer: GCF of Numerators as per given numbers 175/354, 222/784 is
GCF of Numerators i.e. for 175,222 is 1
LCM of denominators i.e. for 354,784 is 138768.
Thus, GCF of Fractions is 1/138768.Finally, GCF of Fractions for 175/354, 222/784 is 1/138768.