GCF of 520/43, 420/559
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 520/43, 420/559 i.e 20/559 easily. The following is the detailed procedure to determine the greatest common factor of fractions 520/43, 420/559.
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 520/43,420/559?
Given fractions are 520/43,420/559
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 520/43,420/559, numerators are 520,420
Denominators are 43,559
The GCF of 520,420 is 20 .
LCM of 43,559 is 559.
The greatest common factor of 520/43,420/559 = [GCF of 520,420]/[LCM of 43,559]= 20/559
Therefore, the GCF of 520/43,420/559 is 20/559.
To find the highest common factor of 520,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
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 520,420 is 20.
Lets's calculate GCF of 520,420
| 2 | 520, 420 |
| 2 | 260, 210 |
| 5 | 130, 105 |
| 26, 21 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 520,420 By Matching Biggest Common Factor Method
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
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 520,420 . The biggest common factor number is the GCF number.
So the greatest common factor 520,420 is 20.
Lets's calculate LCM of 43,559
| 43 | 43, 559 |
| 1, 13 |
∴ So the LCM of the given numbers is 43 x 1 x 13 = 559
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/559
Therefore, the GCF of Fractions 520/43,420/559 is 20/559
Least Common Multiple of 43,559 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 43,559 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(43,559) = 43
common factors(in case of two or more numbers have common factors) = 1
GCF(43,559) x common factors =43 x 1 = 43
LCM(43,559) = ( 43 × 559 ) / 43
LCM(43,559) = 24037 / 43
LCM(43,559) = 559
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 520/43, 420/559
1. What is the HCF of 520,420?
The HCF of 520,420 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 520/43, 420/559?
Answer: GCF of Numerators as per given numbers 520/43, 420/559 is
GCF of Numerators i.e. for 520,420 is 20
LCM of denominators i.e. for 43,559 is 559.
Thus, GCF of Fractions is 20/559.Finally, GCF of Fractions for 520/43, 420/559 is 20/559.