GCF of 510/821, 765/179
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 510/821, 765/179 i.e 255/146959 easily. The following is the detailed procedure to determine the greatest common factor of fractions 510/821, 765/179.
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 510/821,765/179?
Given fractions are 510/821,765/179
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 510/821,765/179, numerators are 510,765
Denominators are 821,179
The GCF of 510,765 is 255 .
LCM of 821,179 is 146959.
The greatest common factor of 510/821,765/179 = [GCF of 510,765]/[LCM of 821,179]= 255/146959
Therefore, the GCF of 510/821,765/179 is 255/146959.
To find the highest common factor of 510,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 510,765 is 255.
Lets's calculate GCF of 510,765
| 3 | 510, 765 |
| 5 | 170, 255 |
| 17 | 34, 51 |
| 2, 3 |
∴ So the GCF of the given numbers is 3 x 5 x 17 = 255
Greatest Common Factor of 510,765 By Matching Biggest Common Factor Method
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
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 510,765 . The biggest common factor number is the GCF number.
So the greatest common factor 510,765 is 255.
Lets's calculate LCM of 821,179
Given numbers has no common factors except 1. So, there LCM is their product i.e 146959
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 255/146959
Therefore, the GCF of Fractions 510/821,765/179 is 255/146959
Least Common Multiple of 821,179 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 821,179 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(821,179) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(821,179) x common factors =1 x 1 = 1
LCM(821,179) = ( 821 × 179 ) / 1
LCM(821,179) = 146959 / 1
LCM(821,179) = 146959
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FAQs on GCF of Fractions of 510/821, 765/179
1. What is the HCF of 510,765?
The HCF of 510,765 is 255
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 510/821, 765/179?
Answer: GCF of Numerators as per given numbers 510/821, 765/179 is
GCF of Numerators i.e. for 510,765 is 255
LCM of denominators i.e. for 821,179 is 146959.
Thus, GCF of Fractions is 255/146959.Finally, GCF of Fractions for 510/821, 765/179 is 255/146959.