Use our free GCF of Fractions Calculator tool to compute the GCF of 77/13, 440/35, 649/151 i.e 11/68705 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/13, 440/35, 649/151.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/13,440/35,649/151
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 77/13,440/35,649/151, numerators are 77,440,649
Denominators are 13,35,151
The GCF of 77,440,649 is 11 .
LCM of 13,35,151 is 68705.
The greatest common factor of 77/13,440/35,649/151 = [GCF of 77,440,649]/[LCM of 13,35,151]= 11/68705
Therefore, the GCF of 77/13,440/35,649/151 is 11/68705.
To find the highest common factor of 77,440,649, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440
The factors of 649 are 1, 11, 59, 649
The HCF of 77,440,649 is 11.
Lets's calculate GCF of 77,440,649
11 | 77, 440, 649 |
7, 40, 59 |
∴ So the GCF of the given numbers is 11 = 11
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 440
:1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440
Now, list down the factors of 649
:1,11,59,649
Greatest Common Factor
We found the factors 77,440,649 . The biggest common factor number is the GCF number.
So the greatest common factor 77,440,649 is 11.
Lets's calculate LCM of 13,35,151
Given numbers has no common factors except 1. So, there LCM is their product i.e 68705
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/68705
Therefore, the GCF of Fractions 77/13,440/35,649/151 is 11/68705
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 13,35,151 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,35,151) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(13,35,151) x common factors =1 x 1 = 1
LCM(13,35,151) = ( 13 × 35 × 151 ) / 1
LCM(13,35,151) = 68705 / 1
LCM(13,35,151) = 68705
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 77,440,649?
The HCF of 77,440,649 is 11
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 77/13, 440/35, 649/151?
Answer: GCF of Numerators as per given numbers 77/13, 440/35, 649/151 is
GCF of Numerators i.e. for 77,440,649 is 11
LCM of denominators i.e. for 13,35,151 is 68705.
Thus, GCF of Fractions is 11/68705.Finally, GCF of Fractions for 77/13, 440/35, 649/151 is 11/68705.