GCF of 583/10, 420/412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 583/10, 420/412 i.e 1/2060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 583/10, 420/412.
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 583/10,420/412?
Given fractions are 583/10,420/412
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 583/10,420/412, numerators are 583,420
Denominators are 10,412
The GCF of 583,420 is 1 .
LCM of 10,412 is 2060.
The greatest common factor of 583/10,420/412 = [GCF of 583,420]/[LCM of 10,412]= 1/2060
Therefore, the GCF of 583/10,420/412 is 1/2060.
To find the highest common factor of 583,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 583 are 1, 11, 53, 583
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 583,420 is 1.
Lets's calculate GCF of 583,420
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 583,420 By Matching Biggest Common Factor Method
Now, list down the factors of 583
:1,11,53,583
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 583,420 . The biggest common factor number is the GCF number.
So the greatest common factor 583,420 is 1.
Lets's calculate LCM of 10,412
| 2 | 10, 412 |
| 5, 206 |
∴ So the LCM of the given numbers is 2 x 5 x 206 = 2060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2060
Therefore, the GCF of Fractions 583/10,420/412 is 1/2060
Least Common Multiple of 10,412 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 10,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,412) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(10,412) x common factors =2 x 1 = 2
LCM(10,412) = ( 10 × 412 ) / 2
LCM(10,412) = 4120 / 2
LCM(10,412) = 2060
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FAQs on GCF of Fractions of 583/10, 420/412
1. What is the HCF of 583,420?
The HCF of 583,420 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 583/10, 420/412?
Answer: GCF of Numerators as per given numbers 583/10, 420/412 is
GCF of Numerators i.e. for 583,420 is 1
LCM of denominators i.e. for 10,412 is 2060.
Thus, GCF of Fractions is 1/2060.Finally, GCF of Fractions for 583/10, 420/412 is 1/2060.