GCF of 305/75, 654/65, 274/81
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 305/75, 654/65, 274/81 i.e 1/26325 easily. The following is the detailed procedure to determine the greatest common factor of fractions 305/75, 654/65, 274/81.
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 305/75,654/65,274/81?
Given fractions are 305/75,654/65,274/81
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 305/75,654/65,274/81, numerators are 305,654,274
Denominators are 75,65,81
The GCF of 305,654,274 is 1 .
LCM of 75,65,81 is 26325.
The greatest common factor of 305/75,654/65,274/81 = [GCF of 305,654,274]/[LCM of 75,65,81]= 1/26325
Therefore, the GCF of 305/75,654/65,274/81 is 1/26325.
To find the highest common factor of 305,654,274, we have to find the factors of both numbers and list the highest common factor.
The factors of 305 are 1, 5, 61, 305
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 274 are 1, 2, 137, 274
The HCF of 305,654,274 is 1.
Lets's calculate GCF of 305,654,274
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 305,654,274 By Matching Biggest Common Factor Method
Now, list down the factors of 305
:1,5,61,305
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 274
:1,2,137,274
Greatest Common Factor
We found the factors 305,654,274 . The biggest common factor number is the GCF number.
So the greatest common factor 305,654,274 is 1.
Lets's calculate LCM of 75,65,81
| 3 | 75, 65, 81 |
| 5 | 25, 65, 27 |
| 5, 13, 27 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 13 x 27 = 26325
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26325
Therefore, the GCF of Fractions 305/75,654/65,274/81 is 1/26325
Least Common Multiple of 75,65,81 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 75,65,81 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,65,81) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(75,65,81) x common factors =1 x 15 = 15
LCM(75,65,81) = ( 75 × 65 × 81 ) / 15
LCM(75,65,81) = 394875 / 15
LCM(75,65,81) = 26325
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FAQs on GCF of Fractions of 305/75, 654/65, 274/81
1. What is the HCF of 305,654,274?
The HCF of 305,654,274 is 1
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 305/75, 654/65, 274/81?
Answer: GCF of Numerators as per given numbers 305/75, 654/65, 274/81 is
GCF of Numerators i.e. for 305,654,274 is 1
LCM of denominators i.e. for 75,65,81 is 26325.
Thus, GCF of Fractions is 1/26325.Finally, GCF of Fractions for 305/75, 654/65, 274/81 is 1/26325.