GCF of 2010/814, 2241/2974
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2010/814, 2241/2974 i.e 3/1210418 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2010/814, 2241/2974.
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 2010/814,2241/2974?
Given fractions are 2010/814,2241/2974
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 2010/814,2241/2974, numerators are 2010,2241
Denominators are 814,2974
The GCF of 2010,2241 is 3 .
LCM of 814,2974 is 1210418.
The greatest common factor of 2010/814,2241/2974 = [GCF of 2010,2241]/[LCM of 814,2974]= 3/1210418
Therefore, the GCF of 2010/814,2241/2974 is 3/1210418.
To find the highest common factor of 2010,2241, we have to find the factors of both numbers and list the highest common factor.
The factors of 2010 are 1, 2, 3, 5, 6, 10, 15, 30, 67, 134, 201, 335, 402, 670, 1005, 2010
The factors of 2241 are 1, 3, 9, 27, 83, 249, 747, 2241
The HCF of 2010,2241 is 3.
Lets's calculate GCF of 2010,2241
| 3 | 2010, 2241 |
| 670, 747 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2010,2241 By Matching Biggest Common Factor Method
Now, list down the factors of 2010
:1,2,3,5,6,10,15,30,67,134,201,335,402,670,1005,2010
Now, list down the factors of 2241
:1,3,9,27,83,249,747,2241
Greatest Common Factor
We found the factors 2010,2241 . The biggest common factor number is the GCF number.
So the greatest common factor 2010,2241 is 3.
Lets's calculate LCM of 814,2974
| 2 | 814, 2974 |
| 407, 1487 |
∴ So the LCM of the given numbers is 2 x 407 x 1487 = 1210418
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1210418
Therefore, the GCF of Fractions 2010/814,2241/2974 is 3/1210418
Least Common Multiple of 814,2974 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 814,2974 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(814,2974) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(814,2974) x common factors =2 x 1 = 2
LCM(814,2974) = ( 814 × 2974 ) / 2
LCM(814,2974) = 2420836 / 2
LCM(814,2974) = 1210418
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FAQs on GCF of Fractions of 2010/814, 2241/2974
1. What is the HCF of 2010,2241?
The HCF of 2010,2241 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 2010/814, 2241/2974?
Answer: GCF of Numerators as per given numbers 2010/814, 2241/2974 is
GCF of Numerators i.e. for 2010,2241 is 3
LCM of denominators i.e. for 814,2974 is 1210418.
Thus, GCF of Fractions is 3/1210418.Finally, GCF of Fractions for 2010/814, 2241/2974 is 3/1210418.