GCF of 39/80, 17/75, 768/684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 39/80, 17/75, 768/684 i.e 1/68400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 39/80, 17/75, 768/684.
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 39/80,17/75,768/684?
Given fractions are 39/80,17/75,768/684
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 39/80,17/75,768/684, numerators are 39,17,768
Denominators are 80,75,684
The GCF of 39,17,768 is 1 .
LCM of 80,75,684 is 68400.
The greatest common factor of 39/80,17/75,768/684 = [GCF of 39,17,768]/[LCM of 80,75,684]= 1/68400
Therefore, the GCF of 39/80,17/75,768/684 is 1/68400.
To find the highest common factor of 39,17,768, we have to find the factors of both numbers and list the highest common factor.
The factors of 39 are 1, 3, 13, 39
The factors of 17 are 1, 17
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The HCF of 39,17,768 is 1.
Lets's calculate GCF of 39,17,768
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 39,17,768 By Matching Biggest Common Factor Method
Now, list down the factors of 39
:1,3,13,39
Now, list down the factors of 17
:1,17
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Greatest Common Factor
We found the factors 39,17,768 . The biggest common factor number is the GCF number.
So the greatest common factor 39,17,768 is 1.
Lets's calculate LCM of 80,75,684
| 2 | 80, 75, 684 |
| 2 | 40, 75, 342 |
| 3 | 20, 75, 171 |
| 5 | 20, 25, 57 |
| 4, 5, 57 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 4 x 5 x 57 = 68400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/68400
Therefore, the GCF of Fractions 39/80,17/75,768/684 is 1/68400
Least Common Multiple of 80,75,684 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 80,75,684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(80,75,684) = 1
common factors(in case of two or more numbers have common factors) = 60
GCF(80,75,684) x common factors =1 x 60 = 60
LCM(80,75,684) = ( 80 × 75 × 684 ) / 60
LCM(80,75,684) = 4104000 / 60
LCM(80,75,684) = 68400
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FAQs on GCF of Fractions of 39/80, 17/75, 768/684
1. What is the HCF of 39,17,768?
The HCF of 39,17,768 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 39/80, 17/75, 768/684?
Answer: GCF of Numerators as per given numbers 39/80, 17/75, 768/684 is
GCF of Numerators i.e. for 39,17,768 is 1
LCM of denominators i.e. for 80,75,684 is 68400.
Thus, GCF of Fractions is 1/68400.Finally, GCF of Fractions for 39/80, 17/75, 768/684 is 1/68400.