GCF of 543/15, 420/313
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 543/15, 420/313 i.e 3/4695 easily. The following is the detailed procedure to determine the greatest common factor of fractions 543/15, 420/313.
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 543/15,420/313?
Given fractions are 543/15,420/313
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 543/15,420/313, numerators are 543,420
Denominators are 15,313
The GCF of 543,420 is 3 .
LCM of 15,313 is 4695.
The greatest common factor of 543/15,420/313 = [GCF of 543,420]/[LCM of 15,313]= 3/4695
Therefore, the GCF of 543/15,420/313 is 3/4695.
To find the highest common factor of 543,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 543 are 1, 3, 181, 543
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 543,420 is 3.
Lets's calculate GCF of 543,420
| 3 | 543, 420 |
| 181, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 543,420 By Matching Biggest Common Factor Method
Now, list down the factors of 543
:1,3,181,543
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 543,420 . The biggest common factor number is the GCF number.
So the greatest common factor 543,420 is 3.
Lets's calculate LCM of 15,313
Given numbers has no common factors except 1. So, there LCM is their product i.e 4695
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/4695
Therefore, the GCF of Fractions 543/15,420/313 is 3/4695
Least Common Multiple of 15,313 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 15,313 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,313) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(15,313) x common factors =1 x 1 = 1
LCM(15,313) = ( 15 × 313 ) / 1
LCM(15,313) = 4695 / 1
LCM(15,313) = 4695
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FAQs on GCF of Fractions of 543/15, 420/313
1. What is the HCF of 543,420?
The HCF of 543,420 is 3
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 543/15, 420/313?
Answer: GCF of Numerators as per given numbers 543/15, 420/313 is
GCF of Numerators i.e. for 543,420 is 3
LCM of denominators i.e. for 15,313 is 4695.
Thus, GCF of Fractions is 3/4695.Finally, GCF of Fractions for 543/15, 420/313 is 3/4695.