GCF of 659/54, 678/966
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 659/54, 678/966 i.e 1/8694 easily. The following is the detailed procedure to determine the greatest common factor of fractions 659/54, 678/966.
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 659/54,678/966?
Given fractions are 659/54,678/966
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 659/54,678/966, numerators are 659,678
Denominators are 54,966
The GCF of 659,678 is 1 .
LCM of 54,966 is 8694.
The greatest common factor of 659/54,678/966 = [GCF of 659,678]/[LCM of 54,966]= 1/8694
Therefore, the GCF of 659/54,678/966 is 1/8694.
To find the highest common factor of 659,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 659 are 1, 659
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 659,678 is 1.
Lets's calculate GCF of 659,678
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 659,678 By Matching Biggest Common Factor Method
Now, list down the factors of 659
:1,659
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 659,678 . The biggest common factor number is the GCF number.
So the greatest common factor 659,678 is 1.
Lets's calculate LCM of 54,966
| 2 | 54, 966 |
| 3 | 27, 483 |
| 9, 161 |
∴ So the LCM of the given numbers is 2 x 3 x 9 x 161 = 8694
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8694
Therefore, the GCF of Fractions 659/54,678/966 is 1/8694
Least Common Multiple of 54,966 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 54,966 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,966) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(54,966) x common factors =6 x 1 = 6
LCM(54,966) = ( 54 × 966 ) / 6
LCM(54,966) = 52164 / 6
LCM(54,966) = 8694
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FAQs on GCF of Fractions of 659/54, 678/966
1. What is the HCF of 659,678?
The HCF of 659,678 is 1
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 659/54, 678/966?
Answer: GCF of Numerators as per given numbers 659/54, 678/966 is
GCF of Numerators i.e. for 659,678 is 1
LCM of denominators i.e. for 54,966 is 8694.
Thus, GCF of Fractions is 1/8694.Finally, GCF of Fractions for 659/54, 678/966 is 1/8694.