GCF of 71/45, 42/96, 75/65
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 71/45, 42/96, 75/65 i.e 1/18720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 71/45, 42/96, 75/65.
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 71/45,42/96,75/65?
Given fractions are 71/45,42/96,75/65
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 71/45,42/96,75/65, numerators are 71,42,75
Denominators are 45,96,65
The GCF of 71,42,75 is 1 .
LCM of 45,96,65 is 18720.
The greatest common factor of 71/45,42/96,75/65 = [GCF of 71,42,75]/[LCM of 45,96,65]= 1/18720
Therefore, the GCF of 71/45,42/96,75/65 is 1/18720.
To find the highest common factor of 71,42,75, we have to find the factors of both numbers and list the highest common factor.
The factors of 71 are 1, 71
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 75 are 1, 3, 5, 15, 25, 75
The HCF of 71,42,75 is 1.
Lets's calculate GCF of 71,42,75
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 71,42,75 By Matching Biggest Common Factor Method
Now, list down the factors of 71
:1,71
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 75
:1,3,5,15,25,75
Greatest Common Factor
We found the factors 71,42,75 . The biggest common factor number is the GCF number.
So the greatest common factor 71,42,75 is 1.
Lets's calculate LCM of 45,96,65
| 3 | 45, 96, 65 |
| 5 | 15, 32, 65 |
| 3, 32, 13 |
∴ So the LCM of the given numbers is 3 x 5 x 3 x 32 x 13 = 18720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/18720
Therefore, the GCF of Fractions 71/45,42/96,75/65 is 1/18720
Least Common Multiple of 45,96,65 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 45,96,65 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,96,65) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(45,96,65) x common factors =1 x 15 = 15
LCM(45,96,65) = ( 45 × 96 × 65 ) / 15
LCM(45,96,65) = 280800 / 15
LCM(45,96,65) = 18720
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FAQs on GCF of Fractions of 71/45, 42/96, 75/65
1. What is the HCF of 71,42,75?
The HCF of 71,42,75 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 71/45, 42/96, 75/65?
Answer: GCF of Numerators as per given numbers 71/45, 42/96, 75/65 is
GCF of Numerators i.e. for 71,42,75 is 1
LCM of denominators i.e. for 45,96,65 is 18720.
Thus, GCF of Fractions is 1/18720.Finally, GCF of Fractions for 71/45, 42/96, 75/65 is 1/18720.