GCF of 567/19, 405/755
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 567/19, 405/755 i.e 81/14345 easily. The following is the detailed procedure to determine the greatest common factor of fractions 567/19, 405/755.
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 567/19,405/755?
Given fractions are 567/19,405/755
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 567/19,405/755, numerators are 567,405
Denominators are 19,755
The GCF of 567,405 is 81 .
LCM of 19,755 is 14345.
The greatest common factor of 567/19,405/755 = [GCF of 567,405]/[LCM of 19,755]= 81/14345
Therefore, the GCF of 567/19,405/755 is 81/14345.
To find the highest common factor of 567,405, we have to find the factors of both numbers and list the highest common factor.
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The HCF of 567,405 is 81.
Lets's calculate GCF of 567,405
| 3 | 567, 405 |
| 3 | 189, 135 |
| 3 | 63, 45 |
| 3 | 21, 15 |
| 7, 5 |
∴ So the GCF of the given numbers is 3 x 3 x 3 x 3 = 81
Greatest Common Factor of 567,405 By Matching Biggest Common Factor Method
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Greatest Common Factor
We found the factors 567,405 . The biggest common factor number is the GCF number.
So the greatest common factor 567,405 is 81.
Lets's calculate LCM of 19,755
Given numbers has no common factors except 1. So, there LCM is their product i.e 14345
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 81/14345
Therefore, the GCF of Fractions 567/19,405/755 is 81/14345
Least Common Multiple of 19,755 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 19,755 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,755) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(19,755) x common factors =1 x 1 = 1
LCM(19,755) = ( 19 × 755 ) / 1
LCM(19,755) = 14345 / 1
LCM(19,755) = 14345
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FAQs on GCF of Fractions of 567/19, 405/755
1. What is the HCF of 567,405?
The HCF of 567,405 is 81
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 567/19, 405/755?
Answer: GCF of Numerators as per given numbers 567/19, 405/755 is
GCF of Numerators i.e. for 567,405 is 81
LCM of denominators i.e. for 19,755 is 14345.
Thus, GCF of Fractions is 81/14345.Finally, GCF of Fractions for 567/19, 405/755 is 81/14345.