GCF of 40/78, 75/39, 59/99, 20/76
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/78, 75/39, 59/99, 20/76 i.e 1/97812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/78, 75/39, 59/99, 20/76.
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 40/78,75/39,59/99,20/76?
Given fractions are 40/78,75/39,59/99,20/76
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 40/78,75/39,59/99,20/76, numerators are 40,75,59,20
Denominators are 78,39,99,76
The GCF of 40,75,59,20 is 1 .
LCM of 78,39,99,76 is 97812.
The greatest common factor of 40/78,75/39,59/99,20/76 = [GCF of 40,75,59,20]/[LCM of 78,39,99,76]= 1/97812
Therefore, the GCF of 40/78,75/39,59/99,20/76 is 1/97812.
To find the highest common factor of 40,75,59,20, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 59 are 1, 59
The factors of 20 are 1, 2, 4, 5, 10, 20
The HCF of 40,75,59,20 is 1.
Lets's calculate GCF of 40,75,59,20
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,75,59,20 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 59
:1,59
Now, list down the factors of 20
:1,2,4,5,10,20
Greatest Common Factor
We found the factors 40,75,59,20 . The biggest common factor number is the GCF number.
So the greatest common factor 40,75,59,20 is 1.
Lets's calculate LCM of 78,39,99,76
| 2 | 78, 39, 99, 76 |
| 3 | 39, 39, 99, 38 |
| 13 | 13, 13, 33, 38 |
| 1, 1, 33, 38 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 1 x 1 x 33 x 38 = 97812
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/97812
Therefore, the GCF of Fractions 40/78,75/39,59/99,20/76 is 1/97812
Least Common Multiple of 78,39,99,76 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 78,39,99,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,39,99,76) = 1
common factors(in case of two or more numbers have common factors) = 234
GCF(78,39,99,76) x common factors =1 x 234 = 234
LCM(78,39,99,76) = ( 78 × 39 × 99 × 76 ) / 234
LCM(78,39,99,76) = 22888008 / 234
LCM(78,39,99,76) = 97812
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 40/78, 75/39, 59/99, 20/76
1. What is the HCF of 40,75,59,20?
The HCF of 40,75,59,20 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 40/78, 75/39, 59/99, 20/76?
Answer: GCF of Numerators as per given numbers 40/78, 75/39, 59/99, 20/76 is
GCF of Numerators i.e. for 40,75,59,20 is 1
LCM of denominators i.e. for 78,39,99,76 is 97812.
Thus, GCF of Fractions is 1/97812.Finally, GCF of Fractions for 40/78, 75/39, 59/99, 20/76 is 1/97812.