GCF of 180/41, 420/5613
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 180/41, 420/5613 i.e 60/230133 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/41, 420/5613.
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 180/41,420/5613?
Given fractions are 180/41,420/5613
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 180/41,420/5613, numerators are 180,420
Denominators are 41,5613
The GCF of 180,420 is 60 .
LCM of 41,5613 is 230133.
The greatest common factor of 180/41,420/5613 = [GCF of 180,420]/[LCM of 41,5613]= 60/230133
Therefore, the GCF of 180/41,420/5613 is 60/230133.
To find the highest common factor of 180,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
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 180,420 is 60.
Lets's calculate GCF of 180,420
| 2 | 180, 420 |
| 2 | 90, 210 |
| 3 | 45, 105 |
| 5 | 15, 35 |
| 3, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 180,420 By Matching Biggest Common Factor Method
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
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 180,420 . The biggest common factor number is the GCF number.
So the greatest common factor 180,420 is 60.
Lets's calculate LCM of 41,5613
Given numbers has no common factors except 1. So, there LCM is their product i.e 230133
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/230133
Therefore, the GCF of Fractions 180/41,420/5613 is 60/230133
Least Common Multiple of 41,5613 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 41,5613 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(41,5613) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(41,5613) x common factors =1 x 1 = 1
LCM(41,5613) = ( 41 × 5613 ) / 1
LCM(41,5613) = 230133 / 1
LCM(41,5613) = 230133
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FAQs on GCF of Fractions of 180/41, 420/5613
1. What is the HCF of 180,420?
The HCF of 180,420 is 60
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 180/41, 420/5613?
Answer: GCF of Numerators as per given numbers 180/41, 420/5613 is
GCF of Numerators i.e. for 180,420 is 60
LCM of denominators i.e. for 41,5613 is 230133.
Thus, GCF of Fractions is 60/230133.Finally, GCF of Fractions for 180/41, 420/5613 is 60/230133.