GCF of 6138/675, 1254/9690
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6138/675, 1254/9690 i.e 66/436050 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6138/675, 1254/9690.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 6138/675,1254/9690?
Given fractions are 6138/675,1254/9690
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 6138/675,1254/9690, numerators are 6138,1254
Denominators are 675,9690
The GCF of 6138,1254 is 66 .
LCM of 675,9690 is 436050.
The greatest common factor of 6138/675,1254/9690 = [GCF of 6138,1254]/[LCM of 675,9690]= 66/436050
Therefore, the GCF of 6138/675,1254/9690 is 66/436050.
To find the highest common factor of 6138,1254, we have to find the factors of both numbers and list the highest common factor.
The factors of 6138 are 1, 2, 3, 6, 9, 11, 18, 22, 31, 33, 62, 66, 93, 99, 186, 198, 279, 341, 558, 682, 1023, 2046, 3069, 6138
The factors of 1254 are 1, 2, 3, 6, 11, 19, 22, 33, 38, 57, 66, 114, 209, 418, 627, 1254
The HCF of 6138,1254 is 66.
Lets's calculate GCF of 6138,1254
| 2 | 6138, 1254 |
| 3 | 3069, 627 |
| 11 | 1023, 209 |
| 93, 19 |
∴ So the GCF of the given numbers is 2 x 3 x 11 = 66
Greatest Common Factor of 6138,1254 By Matching Biggest Common Factor Method
Now, list down the factors of 6138
:1,2,3,6,9,11,18,22,31,33,62,66,93,99,186,198,279,341,558,682,1023,2046,3069,6138
Now, list down the factors of 1254
:1,2,3,6,11,19,22,33,38,57,66,114,209,418,627,1254
Greatest Common Factor
We found the factors 6138,1254 . The biggest common factor number is the GCF number.
So the greatest common factor 6138,1254 is 66.
Lets's calculate LCM of 675,9690
| 3 | 675, 9690 |
| 5 | 225, 3230 |
| 45, 646 |
∴ So the LCM of the given numbers is 3 x 5 x 45 x 646 = 436050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 66/436050
Therefore, the GCF of Fractions 6138/675,1254/9690 is 66/436050
Least Common Multiple of 675,9690 with GCF Formula
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 675,9690 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(675,9690) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(675,9690) x common factors =15 x 1 = 15
LCM(675,9690) = ( 675 × 9690 ) / 15
LCM(675,9690) = 6540750 / 15
LCM(675,9690) = 436050
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FAQs on GCF of Fractions of 6138/675, 1254/9690
1. What is the HCF of 6138,1254?
The HCF of 6138,1254 is 66
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 6138/675, 1254/9690?
Answer: GCF of Numerators as per given numbers 6138/675, 1254/9690 is
GCF of Numerators i.e. for 6138,1254 is 66
LCM of denominators i.e. for 675,9690 is 436050.
Thus, GCF of Fractions is 66/436050.Finally, GCF of Fractions for 6138/675, 1254/9690 is 66/436050.