GCF of 2314/588, 7241/8352
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2314/588, 7241/8352 i.e 13/409248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2314/588, 7241/8352.
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 2314/588,7241/8352?
Given fractions are 2314/588,7241/8352
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 2314/588,7241/8352, numerators are 2314,7241
Denominators are 588,8352
The GCF of 2314,7241 is 13 .
LCM of 588,8352 is 409248.
The greatest common factor of 2314/588,7241/8352 = [GCF of 2314,7241]/[LCM of 588,8352]= 13/409248
Therefore, the GCF of 2314/588,7241/8352 is 13/409248.
To find the highest common factor of 2314,7241, we have to find the factors of both numbers and list the highest common factor.
The factors of 2314 are 1, 2, 13, 26, 89, 178, 1157, 2314
The factors of 7241 are 1, 13, 557, 7241
The HCF of 2314,7241 is 13.
Lets's calculate GCF of 2314,7241
| 13 | 2314, 7241 |
| 178, 557 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 2314,7241 By Matching Biggest Common Factor Method
Now, list down the factors of 2314
:1,2,13,26,89,178,1157,2314
Now, list down the factors of 7241
:1,13,557,7241
Greatest Common Factor
We found the factors 2314,7241 . The biggest common factor number is the GCF number.
So the greatest common factor 2314,7241 is 13.
Lets's calculate LCM of 588,8352
| 2 | 588, 8352 |
| 2 | 294, 4176 |
| 3 | 147, 2088 |
| 49, 696 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 49 x 696 = 409248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/409248
Therefore, the GCF of Fractions 2314/588,7241/8352 is 13/409248
Least Common Multiple of 588,8352 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 588,8352 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(588,8352) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(588,8352) x common factors =12 x 1 = 12
LCM(588,8352) = ( 588 × 8352 ) / 12
LCM(588,8352) = 4910976 / 12
LCM(588,8352) = 409248
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FAQs on GCF of Fractions of 2314/588, 7241/8352
1. What is the HCF of 2314,7241?
The HCF of 2314,7241 is 13
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 2314/588, 7241/8352?
Answer: GCF of Numerators as per given numbers 2314/588, 7241/8352 is
GCF of Numerators i.e. for 2314,7241 is 13
LCM of denominators i.e. for 588,8352 is 409248.
Thus, GCF of Fractions is 13/409248.Finally, GCF of Fractions for 2314/588, 7241/8352 is 13/409248.