GCF of 559/428, 420/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 559/428, 420/314 i.e 1/67196 easily. The following is the detailed procedure to determine the greatest common factor of fractions 559/428, 420/314.
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 559/428,420/314?
Given fractions are 559/428,420/314
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 559/428,420/314, numerators are 559,420
Denominators are 428,314
The GCF of 559,420 is 1 .
LCM of 428,314 is 67196.
The greatest common factor of 559/428,420/314 = [GCF of 559,420]/[LCM of 428,314]= 1/67196
Therefore, the GCF of 559/428,420/314 is 1/67196.
To find the highest common factor of 559,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 559 are 1, 13, 43, 559
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 559,420 is 1.
Lets's calculate GCF of 559,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 559,420 By Matching Biggest Common Factor Method
Now, list down the factors of 559
:1,13,43,559
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 559,420 . The biggest common factor number is the GCF number.
So the greatest common factor 559,420 is 1.
Lets's calculate LCM of 428,314
| 2 | 428, 314 |
| 214, 157 |
∴ So the LCM of the given numbers is 2 x 214 x 157 = 67196
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/67196
Therefore, the GCF of Fractions 559/428,420/314 is 1/67196
Least Common Multiple of 428,314 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 428,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(428,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(428,314) x common factors =2 x 1 = 2
LCM(428,314) = ( 428 × 314 ) / 2
LCM(428,314) = 134392 / 2
LCM(428,314) = 67196
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FAQs on GCF of Fractions of 559/428, 420/314
1. What is the HCF of 559,420?
The HCF of 559,420 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 559/428, 420/314?
Answer: GCF of Numerators as per given numbers 559/428, 420/314 is
GCF of Numerators i.e. for 559,420 is 1
LCM of denominators i.e. for 428,314 is 67196.
Thus, GCF of Fractions is 1/67196.Finally, GCF of Fractions for 559/428, 420/314 is 1/67196.