Use our free GCF of Fractions Calculator tool to compute the GCF of 185/690, 120/708 i.e 5/81420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 185/690, 120/708.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 185/690,120/708
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 185/690,120/708, numerators are 185,120
Denominators are 690,708
The GCF of 185,120 is 5 .
LCM of 690,708 is 81420.
The greatest common factor of 185/690,120/708 = [GCF of 185,120]/[LCM of 690,708]= 5/81420
Therefore, the GCF of 185/690,120/708 is 5/81420.
To find the highest common factor of 185,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 185 are 1, 5, 37, 185
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 185,120 is 5.
Lets's calculate GCF of 185,120
5 | 185, 120 |
37, 24 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 185
:1,5,37,185
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 185,120 . The biggest common factor number is the GCF number.
So the greatest common factor 185,120 is 5.
Lets's calculate LCM of 690,708
2 | 690, 708 |
3 | 345, 354 |
115, 118 |
∴ So the LCM of the given numbers is 2 x 3 x 115 x 118 = 81420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/81420
Therefore, the GCF of Fractions 185/690,120/708 is 5/81420
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 690,708 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(690,708) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(690,708) x common factors =6 x 1 = 6
LCM(690,708) = ( 690 × 708 ) / 6
LCM(690,708) = 488520 / 6
LCM(690,708) = 81420
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 185,120?
The HCF of 185,120 is 5
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 185/690, 120/708?
Answer: GCF of Numerators as per given numbers 185/690, 120/708 is
GCF of Numerators i.e. for 185,120 is 5
LCM of denominators i.e. for 690,708 is 81420.
Thus, GCF of Fractions is 5/81420.Finally, GCF of Fractions for 185/690, 120/708 is 5/81420.