Use our free GCF of Fractions Calculator tool to compute the GCF of 768/757, 736/755 i.e 32/571535 easily. The following is the detailed procedure to determine the greatest common factor of fractions 768/757, 736/755.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 768/757,736/755
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 768/757,736/755, numerators are 768,736
Denominators are 757,755
The GCF of 768,736 is 32 .
LCM of 757,755 is 571535.
The greatest common factor of 768/757,736/755 = [GCF of 768,736]/[LCM of 757,755]= 32/571535
Therefore, the GCF of 768/757,736/755 is 32/571535.
To find the highest common factor of 768,736, we have to find the factors of both numbers and list the highest common factor.
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The factors of 736 are 1, 2, 4, 8, 16, 23, 32, 46, 92, 184, 368, 736
The HCF of 768,736 is 32.
Lets's calculate GCF of 768,736
2 | 768, 736 |
2 | 384, 368 |
2 | 192, 184 |
2 | 96, 92 |
2 | 48, 46 |
24, 23 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Now, list down the factors of 736
:1,2,4,8,16,23,32,46,92,184,368,736
Greatest Common Factor
We found the factors 768,736 . The biggest common factor number is the GCF number.
So the greatest common factor 768,736 is 32.
Lets's calculate LCM of 757,755
Given numbers has no common factors except 1. So, there LCM is their product i.e 571535
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/571535
Therefore, the GCF of Fractions 768/757,736/755 is 32/571535
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 757,755 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(757,755) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(757,755) x common factors =1 x 1 = 1
LCM(757,755) = ( 757 × 755 ) / 1
LCM(757,755) = 571535 / 1
LCM(757,755) = 571535
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 768,736?
The HCF of 768,736 is 32
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 768/757, 736/755?
Answer: GCF of Numerators as per given numbers 768/757, 736/755 is
GCF of Numerators i.e. for 768,736 is 32
LCM of denominators i.e. for 757,755 is 571535.
Thus, GCF of Fractions is 32/571535.Finally, GCF of Fractions for 768/757, 736/755 is 32/571535.