Use our free GCF of Fractions Calculator tool to compute the GCF of 705/189, 752/838 i.e 47/158382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/189, 752/838.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 705/189,752/838
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 705/189,752/838, numerators are 705,752
Denominators are 189,838
The GCF of 705,752 is 47 .
LCM of 189,838 is 158382.
The greatest common factor of 705/189,752/838 = [GCF of 705,752]/[LCM of 189,838]= 47/158382
Therefore, the GCF of 705/189,752/838 is 47/158382.
To find the highest common factor of 705,752, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752
The HCF of 705,752 is 47.
Lets's calculate GCF of 705,752
47 | 705, 752 |
15, 16 |
∴ So the GCF of the given numbers is 47 = 47
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 752
:1,2,4,8,16,47,94,188,376,752
Greatest Common Factor
We found the factors 705,752 . The biggest common factor number is the GCF number.
So the greatest common factor 705,752 is 47.
Lets's calculate LCM of 189,838
Given numbers has no common factors except 1. So, there LCM is their product i.e 158382
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 47/158382
Therefore, the GCF of Fractions 705/189,752/838 is 47/158382
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 189,838 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(189,838) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(189,838) x common factors =1 x 1 = 1
LCM(189,838) = ( 189 × 838 ) / 1
LCM(189,838) = 158382 / 1
LCM(189,838) = 158382
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 705,752?
The HCF of 705,752 is 47
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 705/189, 752/838?
Answer: GCF of Numerators as per given numbers 705/189, 752/838 is
GCF of Numerators i.e. for 705,752 is 47
LCM of denominators i.e. for 189,838 is 158382.
Thus, GCF of Fractions is 47/158382.Finally, GCF of Fractions for 705/189, 752/838 is 47/158382.