GCF of 688/75, 731/963
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 688/75, 731/963 i.e 43/24075 easily. The following is the detailed procedure to determine the greatest common factor of fractions 688/75, 731/963.
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 688/75,731/963?
Given fractions are 688/75,731/963
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 688/75,731/963, numerators are 688,731
Denominators are 75,963
The GCF of 688,731 is 43 .
LCM of 75,963 is 24075.
The greatest common factor of 688/75,731/963 = [GCF of 688,731]/[LCM of 75,963]= 43/24075
Therefore, the GCF of 688/75,731/963 is 43/24075.
To find the highest common factor of 688,731, we have to find the factors of both numbers and list the highest common factor.
The factors of 688 are 1, 2, 4, 8, 16, 43, 86, 172, 344, 688
The factors of 731 are 1, 17, 43, 731
The HCF of 688,731 is 43.
Lets's calculate GCF of 688,731
| 43 | 688, 731 |
| 16, 17 |
∴ So the GCF of the given numbers is 43 = 43
Greatest Common Factor of 688,731 By Matching Biggest Common Factor Method
Now, list down the factors of 688
:1,2,4,8,16,43,86,172,344,688
Now, list down the factors of 731
:1,17,43,731
Greatest Common Factor
We found the factors 688,731 . The biggest common factor number is the GCF number.
So the greatest common factor 688,731 is 43.
Lets's calculate LCM of 75,963
| 3 | 75, 963 |
| 25, 321 |
∴ So the LCM of the given numbers is 3 x 25 x 321 = 24075
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 43/24075
Therefore, the GCF of Fractions 688/75,731/963 is 43/24075
Least Common Multiple of 75,963 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 75,963 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,963) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(75,963) x common factors =3 x 1 = 3
LCM(75,963) = ( 75 × 963 ) / 3
LCM(75,963) = 72225 / 3
LCM(75,963) = 24075
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FAQs on GCF of Fractions of 688/75, 731/963
1. What is the HCF of 688,731?
The HCF of 688,731 is 43
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 688/75, 731/963?
Answer: GCF of Numerators as per given numbers 688/75, 731/963 is
GCF of Numerators i.e. for 688,731 is 43
LCM of denominators i.e. for 75,963 is 24075.
Thus, GCF of Fractions is 43/24075.Finally, GCF of Fractions for 688/75, 731/963 is 43/24075.