GCF of 7683/509, 8514/721
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7683/509, 8514/721 i.e 3/366989 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7683/509, 8514/721.
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 7683/509,8514/721?
Given fractions are 7683/509,8514/721
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 7683/509,8514/721, numerators are 7683,8514
Denominators are 509,721
The GCF of 7683,8514 is 3 .
LCM of 509,721 is 366989.
The greatest common factor of 7683/509,8514/721 = [GCF of 7683,8514]/[LCM of 509,721]= 3/366989
Therefore, the GCF of 7683/509,8514/721 is 3/366989.
To find the highest common factor of 7683,8514, we have to find the factors of both numbers and list the highest common factor.
The factors of 7683 are 1, 3, 13, 39, 197, 591, 2561, 7683
The factors of 8514 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 43, 66, 86, 99, 129, 198, 258, 387, 473, 774, 946, 1419, 2838, 4257, 8514
The HCF of 7683,8514 is 3.
Lets's calculate GCF of 7683,8514
| 3 | 7683, 8514 |
| 2561, 2838 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7683,8514 By Matching Biggest Common Factor Method
Now, list down the factors of 7683
:1,3,13,39,197,591,2561,7683
Now, list down the factors of 8514
:1,2,3,6,9,11,18,22,33,43,66,86,99,129,198,258,387,473,774,946,1419,2838,4257,8514
Greatest Common Factor
We found the factors 7683,8514 . The biggest common factor number is the GCF number.
So the greatest common factor 7683,8514 is 3.
Lets's calculate LCM of 509,721
Given numbers has no common factors except 1. So, there LCM is their product i.e 366989
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/366989
Therefore, the GCF of Fractions 7683/509,8514/721 is 3/366989
Least Common Multiple of 509,721 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 509,721 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,721) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(509,721) x common factors =1 x 1 = 1
LCM(509,721) = ( 509 × 721 ) / 1
LCM(509,721) = 366989 / 1
LCM(509,721) = 366989
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FAQs on GCF of Fractions of 7683/509, 8514/721
1. What is the HCF of 7683,8514?
The HCF of 7683,8514 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 7683/509, 8514/721?
Answer: GCF of Numerators as per given numbers 7683/509, 8514/721 is
GCF of Numerators i.e. for 7683,8514 is 3
LCM of denominators i.e. for 509,721 is 366989.
Thus, GCF of Fractions is 3/366989.Finally, GCF of Fractions for 7683/509, 8514/721 is 3/366989.