GCF of 102/269, 2470/279
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 102/269, 2470/279 i.e 2/75051 easily. The following is the detailed procedure to determine the greatest common factor of fractions 102/269, 2470/279.
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 102/269,2470/279?
Given fractions are 102/269,2470/279
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 102/269,2470/279, numerators are 102,2470
Denominators are 269,279
The GCF of 102,2470 is 2 .
LCM of 269,279 is 75051.
The greatest common factor of 102/269,2470/279 = [GCF of 102,2470]/[LCM of 269,279]= 2/75051
Therefore, the GCF of 102/269,2470/279 is 2/75051.
To find the highest common factor of 102,2470, we have to find the factors of both numbers and list the highest common factor.
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The factors of 2470 are 1, 2, 5, 10, 13, 19, 26, 38, 65, 95, 130, 190, 247, 494, 1235, 2470
The HCF of 102,2470 is 2.
Lets's calculate GCF of 102,2470
| 2 | 102, 2470 |
| 51, 1235 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 102,2470 By Matching Biggest Common Factor Method
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Now, list down the factors of 2470
:1,2,5,10,13,19,26,38,65,95,130,190,247,494,1235,2470
Greatest Common Factor
We found the factors 102,2470 . The biggest common factor number is the GCF number.
So the greatest common factor 102,2470 is 2.
Lets's calculate LCM of 269,279
Given numbers has no common factors except 1. So, there LCM is their product i.e 75051
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/75051
Therefore, the GCF of Fractions 102/269,2470/279 is 2/75051
Least Common Multiple of 269,279 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 269,279 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,279) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,279) x common factors =1 x 1 = 1
LCM(269,279) = ( 269 × 279 ) / 1
LCM(269,279) = 75051 / 1
LCM(269,279) = 75051
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 102/269, 2470/279
1. What is the HCF of 102,2470?
The HCF of 102,2470 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 102/269, 2470/279?
Answer: GCF of Numerators as per given numbers 102/269, 2470/279 is
GCF of Numerators i.e. for 102,2470 is 2
LCM of denominators i.e. for 269,279 is 75051.
Thus, GCF of Fractions is 2/75051.Finally, GCF of Fractions for 102/269, 2470/279 is 2/75051.