GCF of 674/77, 754/2989
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 674/77, 754/2989 i.e 2/32879 easily. The following is the detailed procedure to determine the greatest common factor of fractions 674/77, 754/2989.
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 674/77,754/2989?
Given fractions are 674/77,754/2989
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 674/77,754/2989, numerators are 674,754
Denominators are 77,2989
The GCF of 674,754 is 2 .
LCM of 77,2989 is 32879.
The greatest common factor of 674/77,754/2989 = [GCF of 674,754]/[LCM of 77,2989]= 2/32879
Therefore, the GCF of 674/77,754/2989 is 2/32879.
To find the highest common factor of 674,754, we have to find the factors of both numbers and list the highest common factor.
The factors of 674 are 1, 2, 337, 674
The factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754
The HCF of 674,754 is 2.
Lets's calculate GCF of 674,754
| 2 | 674, 754 |
| 337, 377 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 674,754 By Matching Biggest Common Factor Method
Now, list down the factors of 674
:1,2,337,674
Now, list down the factors of 754
:1,2,13,26,29,58,377,754
Greatest Common Factor
We found the factors 674,754 . The biggest common factor number is the GCF number.
So the greatest common factor 674,754 is 2.
Lets's calculate LCM of 77,2989
| 7 | 77, 2989 |
| 11, 427 |
∴ So the LCM of the given numbers is 7 x 11 x 427 = 32879
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/32879
Therefore, the GCF of Fractions 674/77,754/2989 is 2/32879
Least Common Multiple of 77,2989 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 77,2989 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,2989) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(77,2989) x common factors =7 x 1 = 7
LCM(77,2989) = ( 77 × 2989 ) / 7
LCM(77,2989) = 230153 / 7
LCM(77,2989) = 32879
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FAQs on GCF of Fractions of 674/77, 754/2989
1. What is the HCF of 674,754?
The HCF of 674,754 is 2
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 674/77, 754/2989?
Answer: GCF of Numerators as per given numbers 674/77, 754/2989 is
GCF of Numerators i.e. for 674,754 is 2
LCM of denominators i.e. for 77,2989 is 32879.
Thus, GCF of Fractions is 2/32879.Finally, GCF of Fractions for 674/77, 754/2989 is 2/32879.