GCF of 185/76, 765/66, 189/85
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 185/76, 765/66, 189/85 i.e 1/213180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 185/76, 765/66, 189/85.
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 185/76,765/66,189/85?
Given fractions are 185/76,765/66,189/85
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 185/76,765/66,189/85, numerators are 185,765,189
Denominators are 76,66,85
The GCF of 185,765,189 is 1 .
LCM of 76,66,85 is 213180.
The greatest common factor of 185/76,765/66,189/85 = [GCF of 185,765,189]/[LCM of 76,66,85]= 1/213180
Therefore, the GCF of 185/76,765/66,189/85 is 1/213180.
To find the highest common factor of 185,765,189, we have to find the factors of both numbers and list the highest common factor.
The factors of 185 are 1, 5, 37, 185
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The factors of 189 are 1, 3, 7, 9, 21, 27, 63, 189
The HCF of 185,765,189 is 1.
Lets's calculate GCF of 185,765,189
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 185,765,189 By Matching Biggest Common Factor Method
Now, list down the factors of 185
:1,5,37,185
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Now, list down the factors of 189
:1,3,7,9,21,27,63,189
Greatest Common Factor
We found the factors 185,765,189 . The biggest common factor number is the GCF number.
So the greatest common factor 185,765,189 is 1.
Lets's calculate LCM of 76,66,85
| 2 | 76, 66, 85 |
| 38, 33, 85 |
∴ So the LCM of the given numbers is 2 x 38 x 33 x 85 = 213180
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/213180
Therefore, the GCF of Fractions 185/76,765/66,189/85 is 1/213180
Least Common Multiple of 76,66,85 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 76,66,85 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,66,85) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(76,66,85) x common factors =1 x 2 = 2
LCM(76,66,85) = ( 76 × 66 × 85 ) / 2
LCM(76,66,85) = 426360 / 2
LCM(76,66,85) = 213180
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FAQs on GCF of Fractions of 185/76, 765/66, 189/85
1. What is the HCF of 185,765,189?
The HCF of 185,765,189 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 185/76, 765/66, 189/85?
Answer: GCF of Numerators as per given numbers 185/76, 765/66, 189/85 is
GCF of Numerators i.e. for 185,765,189 is 1
LCM of denominators i.e. for 76,66,85 is 213180.
Thus, GCF of Fractions is 1/213180.Finally, GCF of Fractions for 185/76, 765/66, 189/85 is 1/213180.