GCF of 7420/217, 5658/195
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7420/217, 5658/195 i.e 2/42315 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7420/217, 5658/195.
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 7420/217,5658/195?
Given fractions are 7420/217,5658/195
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 7420/217,5658/195, numerators are 7420,5658
Denominators are 217,195
The GCF of 7420,5658 is 2 .
LCM of 217,195 is 42315.
The greatest common factor of 7420/217,5658/195 = [GCF of 7420,5658]/[LCM of 217,195]= 2/42315
Therefore, the GCF of 7420/217,5658/195 is 2/42315.
To find the highest common factor of 7420,5658, we have to find the factors of both numbers and list the highest common factor.
The factors of 7420 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 53, 70, 106, 140, 212, 265, 371, 530, 742, 1060, 1484, 1855, 3710, 7420
The factors of 5658 are 1, 2, 3, 6, 23, 41, 46, 69, 82, 123, 138, 246, 943, 1886, 2829, 5658
The HCF of 7420,5658 is 2.
Lets's calculate GCF of 7420,5658
| 2 | 7420, 5658 |
| 3710, 2829 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7420,5658 By Matching Biggest Common Factor Method
Now, list down the factors of 7420
:1,2,4,5,7,10,14,20,28,35,53,70,106,140,212,265,371,530,742,1060,1484,1855,3710,7420
Now, list down the factors of 5658
:1,2,3,6,23,41,46,69,82,123,138,246,943,1886,2829,5658
Greatest Common Factor
We found the factors 7420,5658 . The biggest common factor number is the GCF number.
So the greatest common factor 7420,5658 is 2.
Lets's calculate LCM of 217,195
Given numbers has no common factors except 1. So, there LCM is their product i.e 42315
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/42315
Therefore, the GCF of Fractions 7420/217,5658/195 is 2/42315
Least Common Multiple of 217,195 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 217,195 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,195) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(217,195) x common factors =1 x 1 = 1
LCM(217,195) = ( 217 × 195 ) / 1
LCM(217,195) = 42315 / 1
LCM(217,195) = 42315
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FAQs on GCF of Fractions of 7420/217, 5658/195
1. What is the HCF of 7420,5658?
The HCF of 7420,5658 is 2
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 7420/217, 5658/195?
Answer: GCF of Numerators as per given numbers 7420/217, 5658/195 is
GCF of Numerators i.e. for 7420,5658 is 2
LCM of denominators i.e. for 217,195 is 42315.
Thus, GCF of Fractions is 2/42315.Finally, GCF of Fractions for 7420/217, 5658/195 is 2/42315.