Use our free GCF of Fractions Calculator tool to compute the GCF of 3654/759, 7740/7071 i.e 18/1788963 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3654/759, 7740/7071.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 3654/759,7740/7071
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 3654/759,7740/7071, numerators are 3654,7740
Denominators are 759,7071
The GCF of 3654,7740 is 18 .
LCM of 759,7071 is 1788963.
The greatest common factor of 3654/759,7740/7071 = [GCF of 3654,7740]/[LCM of 759,7071]= 18/1788963
Therefore, the GCF of 3654/759,7740/7071 is 18/1788963.
To find the highest common factor of 3654,7740, we have to find the factors of both numbers and list the highest common factor.
The factors of 3654 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 29, 42, 58, 63, 87, 126, 174, 203, 261, 406, 522, 609, 1218, 1827, 3654
The factors of 7740 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 43, 45, 60, 86, 90, 129, 172, 180, 215, 258, 387, 430, 516, 645, 774, 860, 1290, 1548, 1935, 2580, 3870, 7740
The HCF of 3654,7740 is 18.
Lets's calculate GCF of 3654,7740
2 | 3654, 7740 |
3 | 1827, 3870 |
3 | 609, 1290 |
203, 430 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 3654
:1,2,3,6,7,9,14,18,21,29,42,58,63,87,126,174,203,261,406,522,609,1218,1827,3654
Now, list down the factors of 7740
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,43,45,60,86,90,129,172,180,215,258,387,430,516,645,774,860,1290,1548,1935,2580,3870,7740
Greatest Common Factor
We found the factors 3654,7740 . The biggest common factor number is the GCF number.
So the greatest common factor 3654,7740 is 18.
Lets's calculate LCM of 759,7071
3 | 759, 7071 |
253, 2357 |
∴ So the LCM of the given numbers is 3 x 253 x 2357 = 1788963
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/1788963
Therefore, the GCF of Fractions 3654/759,7740/7071 is 18/1788963
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 759,7071 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(759,7071) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(759,7071) x common factors =3 x 1 = 3
LCM(759,7071) = ( 759 × 7071 ) / 3
LCM(759,7071) = 5366889 / 3
LCM(759,7071) = 1788963
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 3654,7740?
The HCF of 3654,7740 is 18
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 3654/759, 7740/7071?
Answer: GCF of Numerators as per given numbers 3654/759, 7740/7071 is
GCF of Numerators i.e. for 3654,7740 is 18
LCM of denominators i.e. for 759,7071 is 1788963.
Thus, GCF of Fractions is 18/1788963.Finally, GCF of Fractions for 3654/759, 7740/7071 is 18/1788963.