GCF of 523/65, 420/9805
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 523/65, 420/9805 i.e 1/127465 easily. The following is the detailed procedure to determine the greatest common factor of fractions 523/65, 420/9805.
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 523/65,420/9805?
Given fractions are 523/65,420/9805
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 523/65,420/9805, numerators are 523,420
Denominators are 65,9805
The GCF of 523,420 is 1 .
LCM of 65,9805 is 127465.
The greatest common factor of 523/65,420/9805 = [GCF of 523,420]/[LCM of 65,9805]= 1/127465
Therefore, the GCF of 523/65,420/9805 is 1/127465.
To find the highest common factor of 523,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 523 are 1, 523
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 523,420 is 1.
Lets's calculate GCF of 523,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 523,420 By Matching Biggest Common Factor Method
Now, list down the factors of 523
:1,523
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 523,420 . The biggest common factor number is the GCF number.
So the greatest common factor 523,420 is 1.
Lets's calculate LCM of 65,9805
| 5 | 65, 9805 |
| 13, 1961 |
∴ So the LCM of the given numbers is 5 x 13 x 1961 = 127465
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/127465
Therefore, the GCF of Fractions 523/65,420/9805 is 1/127465
Least Common Multiple of 65,9805 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 65,9805 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,9805) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(65,9805) x common factors =5 x 1 = 5
LCM(65,9805) = ( 65 × 9805 ) / 5
LCM(65,9805) = 637325 / 5
LCM(65,9805) = 127465
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FAQs on GCF of Fractions of 523/65, 420/9805
1. What is the HCF of 523,420?
The HCF of 523,420 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 523/65, 420/9805?
Answer: GCF of Numerators as per given numbers 523/65, 420/9805 is
GCF of Numerators i.e. for 523,420 is 1
LCM of denominators i.e. for 65,9805 is 127465.
Thus, GCF of Fractions is 1/127465.Finally, GCF of Fractions for 523/65, 420/9805 is 1/127465.