GCF of 765/735, 219/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 765/735, 219/289 i.e 3/212415 easily. The following is the detailed procedure to determine the greatest common factor of fractions 765/735, 219/289.
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 765/735,219/289?
Given fractions are 765/735,219/289
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 765/735,219/289, numerators are 765,219
Denominators are 735,289
The GCF of 765,219 is 3 .
LCM of 735,289 is 212415.
The greatest common factor of 765/735,219/289 = [GCF of 765,219]/[LCM of 735,289]= 3/212415
Therefore, the GCF of 765/735,219/289 is 3/212415.
To find the highest common factor of 765,219, we have to find the factors of both numbers and list the highest common factor.
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The factors of 219 are 1, 3, 73, 219
The HCF of 765,219 is 3.
Lets's calculate GCF of 765,219
| 3 | 765, 219 |
| 255, 73 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 765,219 By Matching Biggest Common Factor Method
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 219
:1,3,73,219
Greatest Common Factor
We found the factors 765,219 . The biggest common factor number is the GCF number.
So the greatest common factor 765,219 is 3.
Lets's calculate LCM of 735,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 212415
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/212415
Therefore, the GCF of Fractions 765/735,219/289 is 3/212415
Least Common Multiple of 735,289 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 735,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(735,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(735,289) x common factors =1 x 1 = 1
LCM(735,289) = ( 735 × 289 ) / 1
LCM(735,289) = 212415 / 1
LCM(735,289) = 212415
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FAQs on GCF of Fractions of 765/735, 219/289
1. What is the HCF of 765,219?
The HCF of 765,219 is 3
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 765/735, 219/289?
Answer: GCF of Numerators as per given numbers 765/735, 219/289 is
GCF of Numerators i.e. for 765,219 is 3
LCM of denominators i.e. for 735,289 is 212415.
Thus, GCF of Fractions is 3/212415.Finally, GCF of Fractions for 765/735, 219/289 is 3/212415.