GCF of 565/83, 369/46, 345/78
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 565/83, 369/46, 345/78 i.e 1/148902 easily. The following is the detailed procedure to determine the greatest common factor of fractions 565/83, 369/46, 345/78.
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 565/83,369/46,345/78?
Given fractions are 565/83,369/46,345/78
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 565/83,369/46,345/78, numerators are 565,369,345
Denominators are 83,46,78
The GCF of 565,369,345 is 1 .
LCM of 83,46,78 is 148902.
The greatest common factor of 565/83,369/46,345/78 = [GCF of 565,369,345]/[LCM of 83,46,78]= 1/148902
Therefore, the GCF of 565/83,369/46,345/78 is 1/148902.
To find the highest common factor of 565,369,345, we have to find the factors of both numbers and list the highest common factor.
The factors of 565 are 1, 5, 113, 565
The factors of 369 are 1, 3, 9, 41, 123, 369
The factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345
The HCF of 565,369,345 is 1.
Lets's calculate GCF of 565,369,345
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 565,369,345 By Matching Biggest Common Factor Method
Now, list down the factors of 565
:1,5,113,565
Now, list down the factors of 369
:1,3,9,41,123,369
Now, list down the factors of 345
:1,3,5,15,23,69,115,345
Greatest Common Factor
We found the factors 565,369,345 . The biggest common factor number is the GCF number.
So the greatest common factor 565,369,345 is 1.
Lets's calculate LCM of 83,46,78
| 2 | 83, 46, 78 |
| 83, 23, 39 |
∴ So the LCM of the given numbers is 2 x 83 x 23 x 39 = 148902
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/148902
Therefore, the GCF of Fractions 565/83,369/46,345/78 is 1/148902
Least Common Multiple of 83,46,78 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 83,46,78 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,46,78) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(83,46,78) x common factors =1 x 2 = 2
LCM(83,46,78) = ( 83 × 46 × 78 ) / 2
LCM(83,46,78) = 297804 / 2
LCM(83,46,78) = 148902
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FAQs on GCF of Fractions of 565/83, 369/46, 345/78
1. What is the HCF of 565,369,345?
The HCF of 565,369,345 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 565/83, 369/46, 345/78?
Answer: GCF of Numerators as per given numbers 565/83, 369/46, 345/78 is
GCF of Numerators i.e. for 565,369,345 is 1
LCM of denominators i.e. for 83,46,78 is 148902.
Thus, GCF of Fractions is 1/148902.Finally, GCF of Fractions for 565/83, 369/46, 345/78 is 1/148902.