GCF of 77/688, 32/758, 309/851
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 77/688, 32/758, 309/851 i.e 1/221899952 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/688, 32/758, 309/851.
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 77/688,32/758,309/851?
Given fractions are 77/688,32/758,309/851
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 77/688,32/758,309/851, numerators are 77,32,309
Denominators are 688,758,851
The GCF of 77,32,309 is 1 .
LCM of 688,758,851 is 221899952.
The greatest common factor of 77/688,32/758,309/851 = [GCF of 77,32,309]/[LCM of 688,758,851]= 1/221899952
Therefore, the GCF of 77/688,32/758,309/851 is 1/221899952.
To find the highest common factor of 77,32,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 309 are 1, 3, 103, 309
The HCF of 77,32,309 is 1.
Lets's calculate GCF of 77,32,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 77,32,309 By Matching Biggest Common Factor Method
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 77,32,309 . The biggest common factor number is the GCF number.
So the greatest common factor 77,32,309 is 1.
Lets's calculate LCM of 688,758,851
| 2 | 688, 758, 851 |
| 344, 379, 851 |
∴ So the LCM of the given numbers is 2 x 344 x 379 x 851 = 221899952
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/221899952
Therefore, the GCF of Fractions 77/688,32/758,309/851 is 1/221899952
Least Common Multiple of 688,758,851 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 688,758,851 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(688,758,851) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(688,758,851) x common factors =1 x 2 = 2
LCM(688,758,851) = ( 688 × 758 × 851 ) / 2
LCM(688,758,851) = 443799904 / 2
LCM(688,758,851) = 221899952
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FAQs on GCF of Fractions of 77/688, 32/758, 309/851
1. What is the HCF of 77,32,309?
The HCF of 77,32,309 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 77/688, 32/758, 309/851?
Answer: GCF of Numerators as per given numbers 77/688, 32/758, 309/851 is
GCF of Numerators i.e. for 77,32,309 is 1
LCM of denominators i.e. for 688,758,851 is 221899952.
Thus, GCF of Fractions is 1/221899952.Finally, GCF of Fractions for 77/688, 32/758, 309/851 is 1/221899952.