GCF of 687/66, 759/6149
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 687/66, 759/6149 i.e 3/36894 easily. The following is the detailed procedure to determine the greatest common factor of fractions 687/66, 759/6149.
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 687/66,759/6149?
Given fractions are 687/66,759/6149
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 687/66,759/6149, numerators are 687,759
Denominators are 66,6149
The GCF of 687,759 is 3 .
LCM of 66,6149 is 36894.
The greatest common factor of 687/66,759/6149 = [GCF of 687,759]/[LCM of 66,6149]= 3/36894
Therefore, the GCF of 687/66,759/6149 is 3/36894.
To find the highest common factor of 687,759, we have to find the factors of both numbers and list the highest common factor.
The factors of 687 are 1, 3, 229, 687
The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759
The HCF of 687,759 is 3.
Lets's calculate GCF of 687,759
| 3 | 687, 759 |
| 229, 253 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 687,759 By Matching Biggest Common Factor Method
Now, list down the factors of 687
:1,3,229,687
Now, list down the factors of 759
:1,3,11,23,33,69,253,759
Greatest Common Factor
We found the factors 687,759 . The biggest common factor number is the GCF number.
So the greatest common factor 687,759 is 3.
Lets's calculate LCM of 66,6149
| 11 | 66, 6149 |
| 6, 559 |
∴ So the LCM of the given numbers is 11 x 6 x 559 = 36894
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/36894
Therefore, the GCF of Fractions 687/66,759/6149 is 3/36894
Least Common Multiple of 66,6149 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 66,6149 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,6149) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(66,6149) x common factors =11 x 1 = 11
LCM(66,6149) = ( 66 × 6149 ) / 11
LCM(66,6149) = 405834 / 11
LCM(66,6149) = 36894
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FAQs on GCF of Fractions of 687/66, 759/6149
1. What is the HCF of 687,759?
The HCF of 687,759 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 687/66, 759/6149?
Answer: GCF of Numerators as per given numbers 687/66, 759/6149 is
GCF of Numerators i.e. for 687,759 is 3
LCM of denominators i.e. for 66,6149 is 36894.
Thus, GCF of Fractions is 3/36894.Finally, GCF of Fractions for 687/66, 759/6149 is 3/36894.