GCF of 6834/270, 5321/2958
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6834/270, 5321/2958 i.e 17/133110 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6834/270, 5321/2958.
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 6834/270,5321/2958?
Given fractions are 6834/270,5321/2958
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 6834/270,5321/2958, numerators are 6834,5321
Denominators are 270,2958
The GCF of 6834,5321 is 17 .
LCM of 270,2958 is 133110.
The greatest common factor of 6834/270,5321/2958 = [GCF of 6834,5321]/[LCM of 270,2958]= 17/133110
Therefore, the GCF of 6834/270,5321/2958 is 17/133110.
To find the highest common factor of 6834,5321, we have to find the factors of both numbers and list the highest common factor.
The factors of 6834 are 1, 2, 3, 6, 17, 34, 51, 67, 102, 134, 201, 402, 1139, 2278, 3417, 6834
The factors of 5321 are 1, 17, 313, 5321
The HCF of 6834,5321 is 17.
Lets's calculate GCF of 6834,5321
| 17 | 6834, 5321 |
| 402, 313 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 6834,5321 By Matching Biggest Common Factor Method
Now, list down the factors of 6834
:1,2,3,6,17,34,51,67,102,134,201,402,1139,2278,3417,6834
Now, list down the factors of 5321
:1,17,313,5321
Greatest Common Factor
We found the factors 6834,5321 . The biggest common factor number is the GCF number.
So the greatest common factor 6834,5321 is 17.
Lets's calculate LCM of 270,2958
| 2 | 270, 2958 |
| 3 | 135, 1479 |
| 45, 493 |
∴ So the LCM of the given numbers is 2 x 3 x 45 x 493 = 133110
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/133110
Therefore, the GCF of Fractions 6834/270,5321/2958 is 17/133110
Least Common Multiple of 270,2958 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 270,2958 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,2958) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(270,2958) x common factors =6 x 1 = 6
LCM(270,2958) = ( 270 × 2958 ) / 6
LCM(270,2958) = 798660 / 6
LCM(270,2958) = 133110
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FAQs on GCF of Fractions of 6834/270, 5321/2958
1. What is the HCF of 6834,5321?
The HCF of 6834,5321 is 17
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 6834/270, 5321/2958?
Answer: GCF of Numerators as per given numbers 6834/270, 5321/2958 is
GCF of Numerators i.e. for 6834,5321 is 17
LCM of denominators i.e. for 270,2958 is 133110.
Thus, GCF of Fractions is 17/133110.Finally, GCF of Fractions for 6834/270, 5321/2958 is 17/133110.