GCF of 5874/208, 2013/1942
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5874/208, 2013/1942 i.e 33/201968 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5874/208, 2013/1942.
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 5874/208,2013/1942?
Given fractions are 5874/208,2013/1942
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 5874/208,2013/1942, numerators are 5874,2013
Denominators are 208,1942
The GCF of 5874,2013 is 33 .
LCM of 208,1942 is 201968.
The greatest common factor of 5874/208,2013/1942 = [GCF of 5874,2013]/[LCM of 208,1942]= 33/201968
Therefore, the GCF of 5874/208,2013/1942 is 33/201968.
To find the highest common factor of 5874,2013, we have to find the factors of both numbers and list the highest common factor.
The factors of 5874 are 1, 2, 3, 6, 11, 22, 33, 66, 89, 178, 267, 534, 979, 1958, 2937, 5874
The factors of 2013 are 1, 3, 11, 33, 61, 183, 671, 2013
The HCF of 5874,2013 is 33.
Lets's calculate GCF of 5874,2013
| 3 | 5874, 2013 |
| 11 | 1958, 671 |
| 178, 61 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Greatest Common Factor of 5874,2013 By Matching Biggest Common Factor Method
Now, list down the factors of 5874
:1,2,3,6,11,22,33,66,89,178,267,534,979,1958,2937,5874
Now, list down the factors of 2013
:1,3,11,33,61,183,671,2013
Greatest Common Factor
We found the factors 5874,2013 . The biggest common factor number is the GCF number.
So the greatest common factor 5874,2013 is 33.
Lets's calculate LCM of 208,1942
| 2 | 208, 1942 |
| 104, 971 |
∴ So the LCM of the given numbers is 2 x 104 x 971 = 201968
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/201968
Therefore, the GCF of Fractions 5874/208,2013/1942 is 33/201968
Least Common Multiple of 208,1942 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 208,1942 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,1942) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(208,1942) x common factors =2 x 1 = 2
LCM(208,1942) = ( 208 × 1942 ) / 2
LCM(208,1942) = 403936 / 2
LCM(208,1942) = 201968
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FAQs on GCF of Fractions of 5874/208, 2013/1942
1. What is the HCF of 5874,2013?
The HCF of 5874,2013 is 33
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 5874/208, 2013/1942?
Answer: GCF of Numerators as per given numbers 5874/208, 2013/1942 is
GCF of Numerators i.e. for 5874,2013 is 33
LCM of denominators i.e. for 208,1942 is 201968.
Thus, GCF of Fractions is 33/201968.Finally, GCF of Fractions for 5874/208, 2013/1942 is 33/201968.