GCF of 2781/678, 3270/9766
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2781/678, 3270/9766 i.e 3/3310674 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2781/678, 3270/9766.
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 2781/678,3270/9766?
Given fractions are 2781/678,3270/9766
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 2781/678,3270/9766, numerators are 2781,3270
Denominators are 678,9766
The GCF of 2781,3270 is 3 .
LCM of 678,9766 is 3310674.
The greatest common factor of 2781/678,3270/9766 = [GCF of 2781,3270]/[LCM of 678,9766]= 3/3310674
Therefore, the GCF of 2781/678,3270/9766 is 3/3310674.
To find the highest common factor of 2781,3270, we have to find the factors of both numbers and list the highest common factor.
The factors of 2781 are 1, 3, 9, 27, 103, 309, 927, 2781
The factors of 3270 are 1, 2, 3, 5, 6, 10, 15, 30, 109, 218, 327, 545, 654, 1090, 1635, 3270
The HCF of 2781,3270 is 3.
Lets's calculate GCF of 2781,3270
| 3 | 2781, 3270 |
| 927, 1090 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2781,3270 By Matching Biggest Common Factor Method
Now, list down the factors of 2781
:1,3,9,27,103,309,927,2781
Now, list down the factors of 3270
:1,2,3,5,6,10,15,30,109,218,327,545,654,1090,1635,3270
Greatest Common Factor
We found the factors 2781,3270 . The biggest common factor number is the GCF number.
So the greatest common factor 2781,3270 is 3.
Lets's calculate LCM of 678,9766
| 2 | 678, 9766 |
| 339, 4883 |
∴ So the LCM of the given numbers is 2 x 339 x 4883 = 3310674
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3310674
Therefore, the GCF of Fractions 2781/678,3270/9766 is 3/3310674
Least Common Multiple of 678,9766 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 678,9766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,9766) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(678,9766) x common factors =2 x 1 = 2
LCM(678,9766) = ( 678 × 9766 ) / 2
LCM(678,9766) = 6621348 / 2
LCM(678,9766) = 3310674
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FAQs on GCF of Fractions of 2781/678, 3270/9766
1. What is the HCF of 2781,3270?
The HCF of 2781,3270 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 2781/678, 3270/9766?
Answer: GCF of Numerators as per given numbers 2781/678, 3270/9766 is
GCF of Numerators i.e. for 2781,3270 is 3
LCM of denominators i.e. for 678,9766 is 3310674.
Thus, GCF of Fractions is 3/3310674.Finally, GCF of Fractions for 2781/678, 3270/9766 is 3/3310674.