GCF of 7371/196, 6858/561
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7371/196, 6858/561 i.e 27/109956 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7371/196, 6858/561.
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 7371/196,6858/561?
Given fractions are 7371/196,6858/561
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 7371/196,6858/561, numerators are 7371,6858
Denominators are 196,561
The GCF of 7371,6858 is 27 .
LCM of 196,561 is 109956.
The greatest common factor of 7371/196,6858/561 = [GCF of 7371,6858]/[LCM of 196,561]= 27/109956
Therefore, the GCF of 7371/196,6858/561 is 27/109956.
To find the highest common factor of 7371,6858, we have to find the factors of both numbers and list the highest common factor.
The factors of 7371 are 1, 3, 7, 9, 13, 21, 27, 39, 63, 81, 91, 117, 189, 273, 351, 567, 819, 1053, 2457, 7371
The factors of 6858 are 1, 2, 3, 6, 9, 18, 27, 54, 127, 254, 381, 762, 1143, 2286, 3429, 6858
The HCF of 7371,6858 is 27.
Lets's calculate GCF of 7371,6858
| 3 | 7371, 6858 |
| 3 | 2457, 2286 |
| 3 | 819, 762 |
| 273, 254 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 7371,6858 By Matching Biggest Common Factor Method
Now, list down the factors of 7371
:1,3,7,9,13,21,27,39,63,81,91,117,189,273,351,567,819,1053,2457,7371
Now, list down the factors of 6858
:1,2,3,6,9,18,27,54,127,254,381,762,1143,2286,3429,6858
Greatest Common Factor
We found the factors 7371,6858 . The biggest common factor number is the GCF number.
So the greatest common factor 7371,6858 is 27.
Lets's calculate LCM of 196,561
Given numbers has no common factors except 1. So, there LCM is their product i.e 109956
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/109956
Therefore, the GCF of Fractions 7371/196,6858/561 is 27/109956
Least Common Multiple of 196,561 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 196,561 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(196,561) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(196,561) x common factors =1 x 1 = 1
LCM(196,561) = ( 196 × 561 ) / 1
LCM(196,561) = 109956 / 1
LCM(196,561) = 109956
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FAQs on GCF of Fractions of 7371/196, 6858/561
1. What is the HCF of 7371,6858?
The HCF of 7371,6858 is 27
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 7371/196, 6858/561?
Answer: GCF of Numerators as per given numbers 7371/196, 6858/561 is
GCF of Numerators i.e. for 7371,6858 is 27
LCM of denominators i.e. for 196,561 is 109956.
Thus, GCF of Fractions is 27/109956.Finally, GCF of Fractions for 7371/196, 6858/561 is 27/109956.