GCF of 471/30, 420/381
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 471/30, 420/381 i.e 3/3810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 471/30, 420/381.
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 471/30,420/381?
Given fractions are 471/30,420/381
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 471/30,420/381, numerators are 471,420
Denominators are 30,381
The GCF of 471,420 is 3 .
LCM of 30,381 is 3810.
The greatest common factor of 471/30,420/381 = [GCF of 471,420]/[LCM of 30,381]= 3/3810
Therefore, the GCF of 471/30,420/381 is 3/3810.
To find the highest common factor of 471,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 471 are 1, 3, 157, 471
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 471,420 is 3.
Lets's calculate GCF of 471,420
| 3 | 471, 420 |
| 157, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 471,420 By Matching Biggest Common Factor Method
Now, list down the factors of 471
:1,3,157,471
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 471,420 . The biggest common factor number is the GCF number.
So the greatest common factor 471,420 is 3.
Lets's calculate LCM of 30,381
| 3 | 30, 381 |
| 10, 127 |
∴ So the LCM of the given numbers is 3 x 10 x 127 = 3810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3810
Therefore, the GCF of Fractions 471/30,420/381 is 3/3810
Least Common Multiple of 30,381 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 30,381 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,381) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(30,381) x common factors =3 x 1 = 3
LCM(30,381) = ( 30 × 381 ) / 3
LCM(30,381) = 11430 / 3
LCM(30,381) = 3810
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FAQs on GCF of Fractions of 471/30, 420/381
1. What is the HCF of 471,420?
The HCF of 471,420 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 471/30, 420/381?
Answer: GCF of Numerators as per given numbers 471/30, 420/381 is
GCF of Numerators i.e. for 471,420 is 3
LCM of denominators i.e. for 30,381 is 3810.
Thus, GCF of Fractions is 3/3810.Finally, GCF of Fractions for 471/30, 420/381 is 3/3810.