GCF of 314/417, 1728/283
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 314/417, 1728/283 i.e 2/118011 easily. The following is the detailed procedure to determine the greatest common factor of fractions 314/417, 1728/283.
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 314/417,1728/283?
Given fractions are 314/417,1728/283
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 314/417,1728/283, numerators are 314,1728
Denominators are 417,283
The GCF of 314,1728 is 2 .
LCM of 417,283 is 118011.
The greatest common factor of 314/417,1728/283 = [GCF of 314,1728]/[LCM of 417,283]= 2/118011
Therefore, the GCF of 314/417,1728/283 is 2/118011.
To find the highest common factor of 314,1728, we have to find the factors of both numbers and list the highest common factor.
The factors of 314 are 1, 2, 157, 314
The factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728
The HCF of 314,1728 is 2.
Lets's calculate GCF of 314,1728
| 2 | 314, 1728 |
| 157, 864 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 314,1728 By Matching Biggest Common Factor Method
Now, list down the factors of 314
:1,2,157,314
Now, list down the factors of 1728
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,144,192,216,288,432,576,864,1728
Greatest Common Factor
We found the factors 314,1728 . The biggest common factor number is the GCF number.
So the greatest common factor 314,1728 is 2.
Lets's calculate LCM of 417,283
Given numbers has no common factors except 1. So, there LCM is their product i.e 118011
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/118011
Therefore, the GCF of Fractions 314/417,1728/283 is 2/118011
Least Common Multiple of 417,283 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 417,283 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(417,283) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(417,283) x common factors =1 x 1 = 1
LCM(417,283) = ( 417 × 283 ) / 1
LCM(417,283) = 118011 / 1
LCM(417,283) = 118011
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FAQs on GCF of Fractions of 314/417, 1728/283
1. What is the HCF of 314,1728?
The HCF of 314,1728 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 314/417, 1728/283?
Answer: GCF of Numerators as per given numbers 314/417, 1728/283 is
GCF of Numerators i.e. for 314,1728 is 2
LCM of denominators i.e. for 417,283 is 118011.
Thus, GCF of Fractions is 2/118011.Finally, GCF of Fractions for 314/417, 1728/283 is 2/118011.