GCF of 754/682, 514/830
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 754/682, 514/830 i.e 2/283030 easily. The following is the detailed procedure to determine the greatest common factor of fractions 754/682, 514/830.
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 754/682,514/830?
Given fractions are 754/682,514/830
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 754/682,514/830, numerators are 754,514
Denominators are 682,830
The GCF of 754,514 is 2 .
LCM of 682,830 is 283030.
The greatest common factor of 754/682,514/830 = [GCF of 754,514]/[LCM of 682,830]= 2/283030
Therefore, the GCF of 754/682,514/830 is 2/283030.
To find the highest common factor of 754,514, we have to find the factors of both numbers and list the highest common factor.
The factors of 754 are 1, 2, 13, 26, 29, 58, 377, 754
The factors of 514 are 1, 2, 257, 514
The HCF of 754,514 is 2.
Lets's calculate GCF of 754,514
| 2 | 754, 514 |
| 377, 257 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 754,514 By Matching Biggest Common Factor Method
Now, list down the factors of 754
:1,2,13,26,29,58,377,754
Now, list down the factors of 514
:1,2,257,514
Greatest Common Factor
We found the factors 754,514 . The biggest common factor number is the GCF number.
So the greatest common factor 754,514 is 2.
Lets's calculate LCM of 682,830
| 2 | 682, 830 |
| 341, 415 |
∴ So the LCM of the given numbers is 2 x 341 x 415 = 283030
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/283030
Therefore, the GCF of Fractions 754/682,514/830 is 2/283030
Least Common Multiple of 682,830 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 682,830 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(682,830) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(682,830) x common factors =2 x 1 = 2
LCM(682,830) = ( 682 × 830 ) / 2
LCM(682,830) = 566060 / 2
LCM(682,830) = 283030
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FAQs on GCF of Fractions of 754/682, 514/830
1. What is the HCF of 754,514?
The HCF of 754,514 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 754/682, 514/830?
Answer: GCF of Numerators as per given numbers 754/682, 514/830 is
GCF of Numerators i.e. for 754,514 is 2
LCM of denominators i.e. for 682,830 is 283030.
Thus, GCF of Fractions is 2/283030.Finally, GCF of Fractions for 754/682, 514/830 is 2/283030.