Use our free GCF of Fractions Calculator tool to compute the GCF of 66/546, 40/936, 691/765 i.e 1/556920 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/546, 40/936, 691/765.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/546,40/936,691/765
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 66/546,40/936,691/765, numerators are 66,40,691
Denominators are 546,936,765
The GCF of 66,40,691 is 1 .
LCM of 546,936,765 is 556920.
The greatest common factor of 66/546,40/936,691/765 = [GCF of 66,40,691]/[LCM of 546,936,765]= 1/556920
Therefore, the GCF of 66/546,40/936,691/765 is 1/556920.
To find the highest common factor of 66,40,691, we have to find the factors of both numbers and list the highest common factor.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 691 are 1, 691
The HCF of 66,40,691 is 1.
Lets's calculate GCF of 66,40,691
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 691
:1,691
Greatest Common Factor
We found the factors 66,40,691 . The biggest common factor number is the GCF number.
So the greatest common factor 66,40,691 is 1.
Lets's calculate LCM of 546,936,765
2 | 546, 936, 765 |
3 | 273, 468, 765 |
3 | 91, 156, 255 |
13 | 91, 52, 85 |
7, 4, 85 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 13 x 7 x 4 x 85 = 556920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/556920
Therefore, the GCF of Fractions 66/546,40/936,691/765 is 1/556920
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 546,936,765 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,936,765) = 3
common factors(in case of two or more numbers have common factors) = 234
GCF(546,936,765) x common factors =3 x 234 = 702
LCM(546,936,765) = ( 546 × 936 × 765 ) / 702
LCM(546,936,765) = 390957840 / 702
LCM(546,936,765) = 556920
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 66,40,691?
The HCF of 66,40,691 is 1
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 66/546, 40/936, 691/765?
Answer: GCF of Numerators as per given numbers 66/546, 40/936, 691/765 is
GCF of Numerators i.e. for 66,40,691 is 1
LCM of denominators i.e. for 546,936,765 is 556920.
Thus, GCF of Fractions is 1/556920.Finally, GCF of Fractions for 66/546, 40/936, 691/765 is 1/556920.