GCF of 287/207, 5306/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 287/207, 5306/414 i.e 7/414 easily. The following is the detailed procedure to determine the greatest common factor of fractions 287/207, 5306/414.
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 287/207,5306/414?
Given fractions are 287/207,5306/414
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 287/207,5306/414, numerators are 287,5306
Denominators are 207,414
The GCF of 287,5306 is 7 .
LCM of 207,414 is 414.
The greatest common factor of 287/207,5306/414 = [GCF of 287,5306]/[LCM of 207,414]= 7/414
Therefore, the GCF of 287/207,5306/414 is 7/414.
To find the highest common factor of 287,5306, we have to find the factors of both numbers and list the highest common factor.
The factors of 287 are 1, 7, 41, 287
The factors of 5306 are 1, 2, 7, 14, 379, 758, 2653, 5306
The HCF of 287,5306 is 7.
Lets's calculate GCF of 287,5306
| 7 | 287, 5306 |
| 41, 758 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 287,5306 By Matching Biggest Common Factor Method
Now, list down the factors of 287
:1,7,41,287
Now, list down the factors of 5306
:1,2,7,14,379,758,2653,5306
Greatest Common Factor
We found the factors 287,5306 . The biggest common factor number is the GCF number.
So the greatest common factor 287,5306 is 7.
Lets's calculate LCM of 207,414
| 3 | 207, 414 |
| 3 | 69, 138 |
| 23 | 23, 46 |
| 1, 2 |
∴ So the LCM of the given numbers is 3 x 3 x 23 x 1 x 2 = 414
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/414
Therefore, the GCF of Fractions 287/207,5306/414 is 7/414
Least Common Multiple of 207,414 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 207,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(207,414) = 207
common factors(in case of two or more numbers have common factors) = 1
GCF(207,414) x common factors =207 x 1 = 207
LCM(207,414) = ( 207 × 414 ) / 207
LCM(207,414) = 85698 / 207
LCM(207,414) = 414
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FAQs on GCF of Fractions of 287/207, 5306/414
1. What is the HCF of 287,5306?
The HCF of 287,5306 is 7
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 287/207, 5306/414?
Answer: GCF of Numerators as per given numbers 287/207, 5306/414 is
GCF of Numerators i.e. for 287,5306 is 7
LCM of denominators i.e. for 207,414 is 414.
Thus, GCF of Fractions is 7/414.Finally, GCF of Fractions for 287/207, 5306/414 is 7/414.