GCF of 5967/269, 6578/7146
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5967/269, 6578/7146 i.e 13/1922274 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5967/269, 6578/7146.
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 5967/269,6578/7146?
Given fractions are 5967/269,6578/7146
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 5967/269,6578/7146, numerators are 5967,6578
Denominators are 269,7146
The GCF of 5967,6578 is 13 .
LCM of 269,7146 is 1922274.
The greatest common factor of 5967/269,6578/7146 = [GCF of 5967,6578]/[LCM of 269,7146]= 13/1922274
Therefore, the GCF of 5967/269,6578/7146 is 13/1922274.
To find the highest common factor of 5967,6578, we have to find the factors of both numbers and list the highest common factor.
The factors of 5967 are 1, 3, 9, 13, 17, 27, 39, 51, 117, 153, 221, 351, 459, 663, 1989, 5967
The factors of 6578 are 1, 2, 11, 13, 22, 23, 26, 46, 143, 253, 286, 299, 506, 598, 3289, 6578
The HCF of 5967,6578 is 13.
Lets's calculate GCF of 5967,6578
| 13 | 5967, 6578 |
| 459, 506 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 5967,6578 By Matching Biggest Common Factor Method
Now, list down the factors of 5967
:1,3,9,13,17,27,39,51,117,153,221,351,459,663,1989,5967
Now, list down the factors of 6578
:1,2,11,13,22,23,26,46,143,253,286,299,506,598,3289,6578
Greatest Common Factor
We found the factors 5967,6578 . The biggest common factor number is the GCF number.
So the greatest common factor 5967,6578 is 13.
Lets's calculate LCM of 269,7146
Given numbers has no common factors except 1. So, there LCM is their product i.e 1922274
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/1922274
Therefore, the GCF of Fractions 5967/269,6578/7146 is 13/1922274
Least Common Multiple of 269,7146 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 269,7146 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,7146) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,7146) x common factors =1 x 1 = 1
LCM(269,7146) = ( 269 × 7146 ) / 1
LCM(269,7146) = 1922274 / 1
LCM(269,7146) = 1922274
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FAQs on GCF of Fractions of 5967/269, 6578/7146
1. What is the HCF of 5967,6578?
The HCF of 5967,6578 is 13
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 5967/269, 6578/7146?
Answer: GCF of Numerators as per given numbers 5967/269, 6578/7146 is
GCF of Numerators i.e. for 5967,6578 is 13
LCM of denominators i.e. for 269,7146 is 1922274.
Thus, GCF of Fractions is 13/1922274.Finally, GCF of Fractions for 5967/269, 6578/7146 is 13/1922274.