GCF of 41/81, 96/70, 17/27, 85/65
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 41/81, 96/70, 17/27, 85/65 i.e 1/73710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 41/81, 96/70, 17/27, 85/65.
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 41/81,96/70,17/27,85/65?
Given fractions are 41/81,96/70,17/27,85/65
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 41/81,96/70,17/27,85/65, numerators are 41,96,17,85
Denominators are 81,70,27,65
The GCF of 41,96,17,85 is 1 .
LCM of 81,70,27,65 is 73710.
The greatest common factor of 41/81,96/70,17/27,85/65 = [GCF of 41,96,17,85]/[LCM of 81,70,27,65]= 1/73710
Therefore, the GCF of 41/81,96/70,17/27,85/65 is 1/73710.
To find the highest common factor of 41,96,17,85, we have to find the factors of both numbers and list the highest common factor.
The factors of 41 are 1, 41
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 17 are 1, 17
The factors of 85 are 1, 5, 17, 85
The HCF of 41,96,17,85 is 1.
Lets's calculate GCF of 41,96,17,85
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 41,96,17,85 By Matching Biggest Common Factor Method
Now, list down the factors of 41
:1,41
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 17
:1,17
Now, list down the factors of 85
:1,5,17,85
Greatest Common Factor
We found the factors 41,96,17,85 . The biggest common factor number is the GCF number.
So the greatest common factor 41,96,17,85 is 1.
Lets's calculate LCM of 81,70,27,65
| 3 | 81, 70, 27, 65 |
| 3 | 27, 70, 9, 65 |
| 3 | 3, 70, 9, 65 |
| 5 | 1, 70, 3, 65 |
| 1, 14, 3, 13 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 5 x 1 x 14 x 3 x 13 = 73710
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/73710
Therefore, the GCF of Fractions 41/81,96/70,17/27,85/65 is 1/73710
Least Common Multiple of 81,70,27,65 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 81,70,27,65 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,70,27,65) = 1
common factors(in case of two or more numbers have common factors) = 135
GCF(81,70,27,65) x common factors =1 x 135 = 135
LCM(81,70,27,65) = ( 81 × 70 × 27 × 65 ) / 135
LCM(81,70,27,65) = 9950850 / 135
LCM(81,70,27,65) = 73710
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 41/81, 96/70, 17/27, 85/65
1. What is the HCF of 41,96,17,85?
The HCF of 41,96,17,85 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 41/81, 96/70, 17/27, 85/65?
Answer: GCF of Numerators as per given numbers 41/81, 96/70, 17/27, 85/65 is
GCF of Numerators i.e. for 41,96,17,85 is 1
LCM of denominators i.e. for 81,70,27,65 is 73710.
Thus, GCF of Fractions is 1/73710.Finally, GCF of Fractions for 41/81, 96/70, 17/27, 85/65 is 1/73710.