GCF of 40/59, 59/88, 319/42
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/59, 59/88, 319/42 i.e 1/109032 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/59, 59/88, 319/42.
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 40/59,59/88,319/42?
Given fractions are 40/59,59/88,319/42
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 40/59,59/88,319/42, numerators are 40,59,319
Denominators are 59,88,42
The GCF of 40,59,319 is 1 .
LCM of 59,88,42 is 109032.
The greatest common factor of 40/59,59/88,319/42 = [GCF of 40,59,319]/[LCM of 59,88,42]= 1/109032
Therefore, the GCF of 40/59,59/88,319/42 is 1/109032.
To find the highest common factor of 40,59,319, 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 59 are 1, 59
The factors of 319 are 1, 11, 29, 319
The HCF of 40,59,319 is 1.
Lets's calculate GCF of 40,59,319
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,59,319 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 59
:1,59
Now, list down the factors of 319
:1,11,29,319
Greatest Common Factor
We found the factors 40,59,319 . The biggest common factor number is the GCF number.
So the greatest common factor 40,59,319 is 1.
Lets's calculate LCM of 59,88,42
| 2 | 59, 88, 42 |
| 59, 44, 21 |
∴ So the LCM of the given numbers is 2 x 59 x 44 x 21 = 109032
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/109032
Therefore, the GCF of Fractions 40/59,59/88,319/42 is 1/109032
Least Common Multiple of 59,88,42 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 59,88,42 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(59,88,42) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(59,88,42) x common factors =1 x 2 = 2
LCM(59,88,42) = ( 59 × 88 × 42 ) / 2
LCM(59,88,42) = 218064 / 2
LCM(59,88,42) = 109032
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FAQs on GCF of Fractions of 40/59, 59/88, 319/42
1. What is the HCF of 40,59,319?
The HCF of 40,59,319 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 40/59, 59/88, 319/42?
Answer: GCF of Numerators as per given numbers 40/59, 59/88, 319/42 is
GCF of Numerators i.e. for 40,59,319 is 1
LCM of denominators i.e. for 59,88,42 is 109032.
Thus, GCF of Fractions is 1/109032.Finally, GCF of Fractions for 40/59, 59/88, 319/42 is 1/109032.