Use our free GCF of Fractions Calculator tool to compute the GCF of 592/188, 352/705 i.e 16/2820 easily. The following is the detailed procedure to determine the greatest common factor of fractions 592/188, 352/705.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 592/188,352/705
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 592/188,352/705, numerators are 592,352
Denominators are 188,705
The GCF of 592,352 is 16 .
LCM of 188,705 is 2820.
The greatest common factor of 592/188,352/705 = [GCF of 592,352]/[LCM of 188,705]= 16/2820
Therefore, the GCF of 592/188,352/705 is 16/2820.
To find the highest common factor of 592,352, we have to find the factors of both numbers and list the highest common factor.
The factors of 592 are 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352
The HCF of 592,352 is 16.
Lets's calculate GCF of 592,352
2 | 592, 352 |
2 | 296, 176 |
2 | 148, 88 |
2 | 74, 44 |
37, 22 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 592
:1,2,4,8,16,37,74,148,296,592
Now, list down the factors of 352
:1,2,4,8,11,16,22,32,44,88,176,352
Greatest Common Factor
We found the factors 592,352 . The biggest common factor number is the GCF number.
So the greatest common factor 592,352 is 16.
Lets's calculate LCM of 188,705
47 | 188, 705 |
4, 15 |
∴ So the LCM of the given numbers is 47 x 4 x 15 = 2820
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/2820
Therefore, the GCF of Fractions 592/188,352/705 is 16/2820
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 188,705 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(188,705) = 47
common factors(in case of two or more numbers have common factors) = 1
GCF(188,705) x common factors =47 x 1 = 47
LCM(188,705) = ( 188 × 705 ) / 47
LCM(188,705) = 132540 / 47
LCM(188,705) = 2820
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 592,352?
The HCF of 592,352 is 16
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 592/188, 352/705?
Answer: GCF of Numerators as per given numbers 592/188, 352/705 is
GCF of Numerators i.e. for 592,352 is 16
LCM of denominators i.e. for 188,705 is 2820.
Thus, GCF of Fractions is 16/2820.Finally, GCF of Fractions for 592/188, 352/705 is 16/2820.