GCF of 5278/189, 3428/218
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5278/189, 3428/218 i.e 2/41202 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5278/189, 3428/218.
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 5278/189,3428/218?
Given fractions are 5278/189,3428/218
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 5278/189,3428/218, numerators are 5278,3428
Denominators are 189,218
The GCF of 5278,3428 is 2 .
LCM of 189,218 is 41202.
The greatest common factor of 5278/189,3428/218 = [GCF of 5278,3428]/[LCM of 189,218]= 2/41202
Therefore, the GCF of 5278/189,3428/218 is 2/41202.
To find the highest common factor of 5278,3428, we have to find the factors of both numbers and list the highest common factor.
The factors of 5278 are 1, 2, 7, 13, 14, 26, 29, 58, 91, 182, 203, 377, 406, 754, 2639, 5278
The factors of 3428 are 1, 2, 4, 857, 1714, 3428
The HCF of 5278,3428 is 2.
Lets's calculate GCF of 5278,3428
| 2 | 5278, 3428 |
| 2639, 1714 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 5278,3428 By Matching Biggest Common Factor Method
Now, list down the factors of 5278
:1,2,7,13,14,26,29,58,91,182,203,377,406,754,2639,5278
Now, list down the factors of 3428
:1,2,4,857,1714,3428
Greatest Common Factor
We found the factors 5278,3428 . The biggest common factor number is the GCF number.
So the greatest common factor 5278,3428 is 2.
Lets's calculate LCM of 189,218
Given numbers has no common factors except 1. So, there LCM is their product i.e 41202
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/41202
Therefore, the GCF of Fractions 5278/189,3428/218 is 2/41202
Least Common Multiple of 189,218 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 189,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(189,218) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(189,218) x common factors =1 x 1 = 1
LCM(189,218) = ( 189 × 218 ) / 1
LCM(189,218) = 41202 / 1
LCM(189,218) = 41202
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FAQs on GCF of Fractions of 5278/189, 3428/218
1. What is the HCF of 5278,3428?
The HCF of 5278,3428 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 5278/189, 3428/218?
Answer: GCF of Numerators as per given numbers 5278/189, 3428/218 is
GCF of Numerators i.e. for 5278,3428 is 2
LCM of denominators i.e. for 189,218 is 41202.
Thus, GCF of Fractions is 2/41202.Finally, GCF of Fractions for 5278/189, 3428/218 is 2/41202.