GCF of 312/38, 273/31, 420/54
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 312/38, 273/31, 420/54 i.e 3/31806 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/38, 273/31, 420/54.
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 312/38,273/31,420/54?
Given fractions are 312/38,273/31,420/54
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 312/38,273/31,420/54, numerators are 312,273,420
Denominators are 38,31,54
The GCF of 312,273,420 is 3 .
LCM of 38,31,54 is 31806.
The greatest common factor of 312/38,273/31,420/54 = [GCF of 312,273,420]/[LCM of 38,31,54]= 3/31806
Therefore, the GCF of 312/38,273/31,420/54 is 3/31806.
To find the highest common factor of 312,273,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 273 are 1, 3, 7, 13, 21, 39, 91, 273
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 312,273,420 is 3.
Lets's calculate GCF of 312,273,420
| 3 | 312, 273, 420 |
| 104, 91, 140 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 312,273,420 By Matching Biggest Common Factor Method
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 273
:1,3,7,13,21,39,91,273
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 312,273,420 . The biggest common factor number is the GCF number.
So the greatest common factor 312,273,420 is 3.
Lets's calculate LCM of 38,31,54
| 2 | 38, 31, 54 |
| 19, 31, 27 |
∴ So the LCM of the given numbers is 2 x 19 x 31 x 27 = 31806
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/31806
Therefore, the GCF of Fractions 312/38,273/31,420/54 is 3/31806
Least Common Multiple of 38,31,54 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 38,31,54 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,31,54) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(38,31,54) x common factors =1 x 2 = 2
LCM(38,31,54) = ( 38 × 31 × 54 ) / 2
LCM(38,31,54) = 63612 / 2
LCM(38,31,54) = 31806
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FAQs on GCF of Fractions of 312/38, 273/31, 420/54
1. What is the HCF of 312,273,420?
The HCF of 312,273,420 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 312/38, 273/31, 420/54?
Answer: GCF of Numerators as per given numbers 312/38, 273/31, 420/54 is
GCF of Numerators i.e. for 312,273,420 is 3
LCM of denominators i.e. for 38,31,54 is 31806.
Thus, GCF of Fractions is 3/31806.Finally, GCF of Fractions for 312/38, 273/31, 420/54 is 3/31806.