GCF of 254/27, 154/1209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 254/27, 154/1209 i.e 2/10881 easily. The following is the detailed procedure to determine the greatest common factor of fractions 254/27, 154/1209.
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 254/27,154/1209?
Given fractions are 254/27,154/1209
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 254/27,154/1209, numerators are 254,154
Denominators are 27,1209
The GCF of 254,154 is 2 .
LCM of 27,1209 is 10881.
The greatest common factor of 254/27,154/1209 = [GCF of 254,154]/[LCM of 27,1209]= 2/10881
Therefore, the GCF of 254/27,154/1209 is 2/10881.
To find the highest common factor of 254,154, we have to find the factors of both numbers and list the highest common factor.
The factors of 254 are 1, 2, 127, 254
The factors of 154 are 1, 2, 7, 11, 14, 22, 77, 154
The HCF of 254,154 is 2.
Lets's calculate GCF of 254,154
| 2 | 254, 154 |
| 127, 77 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 254,154 By Matching Biggest Common Factor Method
Now, list down the factors of 254
:1,2,127,254
Now, list down the factors of 154
:1,2,7,11,14,22,77,154
Greatest Common Factor
We found the factors 254,154 . The biggest common factor number is the GCF number.
So the greatest common factor 254,154 is 2.
Lets's calculate LCM of 27,1209
| 3 | 27, 1209 |
| 9, 403 |
∴ So the LCM of the given numbers is 3 x 9 x 403 = 10881
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10881
Therefore, the GCF of Fractions 254/27,154/1209 is 2/10881
Least Common Multiple of 27,1209 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 27,1209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,1209) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(27,1209) x common factors =3 x 1 = 3
LCM(27,1209) = ( 27 × 1209 ) / 3
LCM(27,1209) = 32643 / 3
LCM(27,1209) = 10881
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FAQs on GCF of Fractions of 254/27, 154/1209
1. What is the HCF of 254,154?
The HCF of 254,154 is 2
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 254/27, 154/1209?
Answer: GCF of Numerators as per given numbers 254/27, 154/1209 is
GCF of Numerators i.e. for 254,154 is 2
LCM of denominators i.e. for 27,1209 is 10881.
Thus, GCF of Fractions is 2/10881.Finally, GCF of Fractions for 254/27, 154/1209 is 2/10881.