Use our free GCF of Fractions Calculator tool to compute the GCF of 792/765, 160/782 i.e 8/35190 easily. The following is the detailed procedure to determine the greatest common factor of fractions 792/765, 160/782.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 792/765,160/782
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 792/765,160/782, numerators are 792,160
Denominators are 765,782
The GCF of 792,160 is 8 .
LCM of 765,782 is 35190.
The greatest common factor of 792/765,160/782 = [GCF of 792,160]/[LCM of 765,782]= 8/35190
Therefore, the GCF of 792/765,160/782 is 8/35190.
To find the highest common factor of 792,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 792 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 132, 198, 264, 396, 792
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 792,160 is 8.
Lets's calculate GCF of 792,160
2 | 792, 160 |
2 | 396, 80 |
2 | 198, 40 |
99, 20 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 792
:1,2,3,4,6,8,9,11,12,18,22,24,33,36,44,66,72,88,99,132,198,264,396,792
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 792,160 . The biggest common factor number is the GCF number.
So the greatest common factor 792,160 is 8.
Lets's calculate LCM of 765,782
17 | 765, 782 |
45, 46 |
∴ So the LCM of the given numbers is 17 x 45 x 46 = 35190
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/35190
Therefore, the GCF of Fractions 792/765,160/782 is 8/35190
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 765,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(765,782) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(765,782) x common factors =17 x 1 = 17
LCM(765,782) = ( 765 × 782 ) / 17
LCM(765,782) = 598230 / 17
LCM(765,782) = 35190
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 792,160?
The HCF of 792,160 is 8
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 792/765, 160/782?
Answer: GCF of Numerators as per given numbers 792/765, 160/782 is
GCF of Numerators i.e. for 792,160 is 8
LCM of denominators i.e. for 765,782 is 35190.
Thus, GCF of Fractions is 8/35190.Finally, GCF of Fractions for 792/765, 160/782 is 8/35190.