GCF of 269/14, 988/1314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 269/14, 988/1314 i.e 1/9198 easily. The following is the detailed procedure to determine the greatest common factor of fractions 269/14, 988/1314.
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 269/14,988/1314?
Given fractions are 269/14,988/1314
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 269/14,988/1314, numerators are 269,988
Denominators are 14,1314
The GCF of 269,988 is 1 .
LCM of 14,1314 is 9198.
The greatest common factor of 269/14,988/1314 = [GCF of 269,988]/[LCM of 14,1314]= 1/9198
Therefore, the GCF of 269/14,988/1314 is 1/9198.
To find the highest common factor of 269,988, we have to find the factors of both numbers and list the highest common factor.
The factors of 269 are 1, 269
The factors of 988 are 1, 2, 4, 13, 19, 26, 38, 52, 76, 247, 494, 988
The HCF of 269,988 is 1.
Lets's calculate GCF of 269,988
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 269,988 By Matching Biggest Common Factor Method
Now, list down the factors of 269
:1,269
Now, list down the factors of 988
:1,2,4,13,19,26,38,52,76,247,494,988
Greatest Common Factor
We found the factors 269,988 . The biggest common factor number is the GCF number.
So the greatest common factor 269,988 is 1.
Lets's calculate LCM of 14,1314
| 2 | 14, 1314 |
| 7, 657 |
∴ So the LCM of the given numbers is 2 x 7 x 657 = 9198
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9198
Therefore, the GCF of Fractions 269/14,988/1314 is 1/9198
Least Common Multiple of 14,1314 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 14,1314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,1314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(14,1314) x common factors =2 x 1 = 2
LCM(14,1314) = ( 14 × 1314 ) / 2
LCM(14,1314) = 18396 / 2
LCM(14,1314) = 9198
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FAQs on GCF of Fractions of 269/14, 988/1314
1. What is the HCF of 269,988?
The HCF of 269,988 is 1
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 269/14, 988/1314?
Answer: GCF of Numerators as per given numbers 269/14, 988/1314 is
GCF of Numerators i.e. for 269,988 is 1
LCM of denominators i.e. for 14,1314 is 9198.
Thus, GCF of Fractions is 1/9198.Finally, GCF of Fractions for 269/14, 988/1314 is 1/9198.