GCF of 27/74, 276/41, 285/421
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 27/74, 276/41, 285/421 i.e 3/1277314 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/74, 276/41, 285/421.
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 27/74,276/41,285/421?
Given fractions are 27/74,276/41,285/421
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 27/74,276/41,285/421, numerators are 27,276,285
Denominators are 74,41,421
The GCF of 27,276,285 is 3 .
LCM of 74,41,421 is 1277314.
The greatest common factor of 27/74,276/41,285/421 = [GCF of 27,276,285]/[LCM of 74,41,421]= 3/1277314
Therefore, the GCF of 27/74,276/41,285/421 is 3/1277314.
To find the highest common factor of 27,276,285, we have to find the factors of both numbers and list the highest common factor.
The factors of 27 are 1, 3, 9, 27
The factors of 276 are 1, 2, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276
The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285
The HCF of 27,276,285 is 3.
Lets's calculate GCF of 27,276,285
| 3 | 27, 276, 285 |
| 9, 92, 95 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 27,276,285 By Matching Biggest Common Factor Method
Now, list down the factors of 27
:1,3,9,27
Now, list down the factors of 276
:1,2,3,4,6,12,23,46,69,92,138,276
Now, list down the factors of 285
:1,3,5,15,19,57,95,285
Greatest Common Factor
We found the factors 27,276,285 . The biggest common factor number is the GCF number.
So the greatest common factor 27,276,285 is 3.
Lets's calculate LCM of 74,41,421
Given numbers has no common factors except 1. So, there LCM is their product i.e 1277314
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1277314
Therefore, the GCF of Fractions 27/74,276/41,285/421 is 3/1277314
Least Common Multiple of 74,41,421 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 74,41,421 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,41,421) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(74,41,421) x common factors =1 x 1 = 1
LCM(74,41,421) = ( 74 × 41 × 421 ) / 1
LCM(74,41,421) = 1277314 / 1
LCM(74,41,421) = 1277314
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FAQs on GCF of Fractions of 27/74, 276/41, 285/421
1. What is the HCF of 27,276,285?
The HCF of 27,276,285 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 27/74, 276/41, 285/421?
Answer: GCF of Numerators as per given numbers 27/74, 276/41, 285/421 is
GCF of Numerators i.e. for 27,276,285 is 3
LCM of denominators i.e. for 74,41,421 is 1277314.
Thus, GCF of Fractions is 3/1277314.Finally, GCF of Fractions for 27/74, 276/41, 285/421 is 3/1277314.