GCF of 2709/214, 3051/7753
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2709/214, 3051/7753 i.e 9/1659142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2709/214, 3051/7753.
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 2709/214,3051/7753?
Given fractions are 2709/214,3051/7753
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 2709/214,3051/7753, numerators are 2709,3051
Denominators are 214,7753
The GCF of 2709,3051 is 9 .
LCM of 214,7753 is 1659142.
The greatest common factor of 2709/214,3051/7753 = [GCF of 2709,3051]/[LCM of 214,7753]= 9/1659142
Therefore, the GCF of 2709/214,3051/7753 is 9/1659142.
To find the highest common factor of 2709,3051, we have to find the factors of both numbers and list the highest common factor.
The factors of 2709 are 1, 3, 7, 9, 21, 43, 63, 129, 301, 387, 903, 2709
The factors of 3051 are 1, 3, 9, 27, 113, 339, 1017, 3051
The HCF of 2709,3051 is 9.
Lets's calculate GCF of 2709,3051
| 3 | 2709, 3051 |
| 3 | 903, 1017 |
| 301, 339 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 2709,3051 By Matching Biggest Common Factor Method
Now, list down the factors of 2709
:1,3,7,9,21,43,63,129,301,387,903,2709
Now, list down the factors of 3051
:1,3,9,27,113,339,1017,3051
Greatest Common Factor
We found the factors 2709,3051 . The biggest common factor number is the GCF number.
So the greatest common factor 2709,3051 is 9.
Lets's calculate LCM of 214,7753
Given numbers has no common factors except 1. So, there LCM is their product i.e 1659142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/1659142
Therefore, the GCF of Fractions 2709/214,3051/7753 is 9/1659142
Least Common Multiple of 214,7753 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 214,7753 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(214,7753) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(214,7753) x common factors =1 x 1 = 1
LCM(214,7753) = ( 214 × 7753 ) / 1
LCM(214,7753) = 1659142 / 1
LCM(214,7753) = 1659142
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FAQs on GCF of Fractions of 2709/214, 3051/7753
1. What is the HCF of 2709,3051?
The HCF of 2709,3051 is 9
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 2709/214, 3051/7753?
Answer: GCF of Numerators as per given numbers 2709/214, 3051/7753 is
GCF of Numerators i.e. for 2709,3051 is 9
LCM of denominators i.e. for 214,7753 is 1659142.
Thus, GCF of Fractions is 9/1659142.Finally, GCF of Fractions for 2709/214, 3051/7753 is 9/1659142.