GCF of 405/77, 765/114
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 405/77, 765/114 i.e 45/8778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 405/77, 765/114.
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 405/77,765/114?
Given fractions are 405/77,765/114
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 405/77,765/114, numerators are 405,765
Denominators are 77,114
The GCF of 405,765 is 45 .
LCM of 77,114 is 8778.
The greatest common factor of 405/77,765/114 = [GCF of 405,765]/[LCM of 77,114]= 45/8778
Therefore, the GCF of 405/77,765/114 is 45/8778.
To find the highest common factor of 405,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 405,765 is 45.
Lets's calculate GCF of 405,765
| 3 | 405, 765 |
| 3 | 135, 255 |
| 5 | 45, 85 |
| 9, 17 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 405,765 By Matching Biggest Common Factor Method
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 405,765 . The biggest common factor number is the GCF number.
So the greatest common factor 405,765 is 45.
Lets's calculate LCM of 77,114
Given numbers has no common factors except 1. So, there LCM is their product i.e 8778
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/8778
Therefore, the GCF of Fractions 405/77,765/114 is 45/8778
Least Common Multiple of 77,114 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 77,114 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,114) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,114) x common factors =1 x 1 = 1
LCM(77,114) = ( 77 × 114 ) / 1
LCM(77,114) = 8778 / 1
LCM(77,114) = 8778
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FAQs on GCF of Fractions of 405/77, 765/114
1. What is the HCF of 405,765?
The HCF of 405,765 is 45
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 405/77, 765/114?
Answer: GCF of Numerators as per given numbers 405/77, 765/114 is
GCF of Numerators i.e. for 405,765 is 45
LCM of denominators i.e. for 77,114 is 8778.
Thus, GCF of Fractions is 45/8778.Finally, GCF of Fractions for 405/77, 765/114 is 45/8778.