GCF of 620/586, 420/405
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 620/586, 420/405 i.e 20/237330 easily. The following is the detailed procedure to determine the greatest common factor of fractions 620/586, 420/405.
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 620/586,420/405?
Given fractions are 620/586,420/405
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 620/586,420/405, numerators are 620,420
Denominators are 586,405
The GCF of 620,420 is 20 .
LCM of 586,405 is 237330.
The greatest common factor of 620/586,420/405 = [GCF of 620,420]/[LCM of 586,405]= 20/237330
Therefore, the GCF of 620/586,420/405 is 20/237330.
To find the highest common factor of 620,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 620 are 1, 2, 4, 5, 10, 20, 31, 62, 124, 155, 310, 620
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 620,420 is 20.
Lets's calculate GCF of 620,420
| 2 | 620, 420 |
| 2 | 310, 210 |
| 5 | 155, 105 |
| 31, 21 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 620,420 By Matching Biggest Common Factor Method
Now, list down the factors of 620
:1,2,4,5,10,20,31,62,124,155,310,620
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 620,420 . The biggest common factor number is the GCF number.
So the greatest common factor 620,420 is 20.
Lets's calculate LCM of 586,405
Given numbers has no common factors except 1. So, there LCM is their product i.e 237330
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/237330
Therefore, the GCF of Fractions 620/586,420/405 is 20/237330
Least Common Multiple of 586,405 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 586,405 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(586,405) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(586,405) x common factors =1 x 1 = 1
LCM(586,405) = ( 586 × 405 ) / 1
LCM(586,405) = 237330 / 1
LCM(586,405) = 237330
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FAQs on GCF of Fractions of 620/586, 420/405
1. What is the HCF of 620,420?
The HCF of 620,420 is 20
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 620/586, 420/405?
Answer: GCF of Numerators as per given numbers 620/586, 420/405 is
GCF of Numerators i.e. for 620,420 is 20
LCM of denominators i.e. for 586,405 is 237330.
Thus, GCF of Fractions is 20/237330.Finally, GCF of Fractions for 620/586, 420/405 is 20/237330.