Use our free GCF of Fractions Calculator tool to compute the GCF of 702/180, 459/326 i.e 27/29340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 702/180, 459/326.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 702/180,459/326
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 702/180,459/326, numerators are 702,459
Denominators are 180,326
The GCF of 702,459 is 27 .
LCM of 180,326 is 29340.
The greatest common factor of 702/180,459/326 = [GCF of 702,459]/[LCM of 180,326]= 27/29340
Therefore, the GCF of 702/180,459/326 is 27/29340.
To find the highest common factor of 702,459, we have to find the factors of both numbers and list the highest common factor.
The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702
The factors of 459 are 1, 3, 9, 17, 27, 51, 153, 459
The HCF of 702,459 is 27.
Lets's calculate GCF of 702,459
3 | 702, 459 |
3 | 234, 153 |
3 | 78, 51 |
26, 17 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 702
:1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702
Now, list down the factors of 459
:1,3,9,17,27,51,153,459
Greatest Common Factor
We found the factors 702,459 . The biggest common factor number is the GCF number.
So the greatest common factor 702,459 is 27.
Lets's calculate LCM of 180,326
2 | 180, 326 |
90, 163 |
∴ So the LCM of the given numbers is 2 x 90 x 163 = 29340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/29340
Therefore, the GCF of Fractions 702/180,459/326 is 27/29340
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 180,326 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(180,326) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(180,326) x common factors =2 x 1 = 2
LCM(180,326) = ( 180 × 326 ) / 2
LCM(180,326) = 58680 / 2
LCM(180,326) = 29340
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 702,459?
The HCF of 702,459 is 27
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 702/180, 459/326?
Answer: GCF of Numerators as per given numbers 702/180, 459/326 is
GCF of Numerators i.e. for 702,459 is 27
LCM of denominators i.e. for 180,326 is 29340.
Thus, GCF of Fractions is 27/29340.Finally, GCF of Fractions for 702/180, 459/326 is 27/29340.