GCF of 9416/349, 5390/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9416/349, 5390/409 i.e 22/142741 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9416/349, 5390/409.
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 9416/349,5390/409?
Given fractions are 9416/349,5390/409
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 9416/349,5390/409, numerators are 9416,5390
Denominators are 349,409
The GCF of 9416,5390 is 22 .
LCM of 349,409 is 142741.
The greatest common factor of 9416/349,5390/409 = [GCF of 9416,5390]/[LCM of 349,409]= 22/142741
Therefore, the GCF of 9416/349,5390/409 is 22/142741.
To find the highest common factor of 9416,5390, we have to find the factors of both numbers and list the highest common factor.
The factors of 9416 are 1, 2, 4, 8, 11, 22, 44, 88, 107, 214, 428, 856, 1177, 2354, 4708, 9416
The factors of 5390 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 49, 55, 70, 77, 98, 110, 154, 245, 385, 490, 539, 770, 1078, 2695, 5390
The HCF of 9416,5390 is 22.
Lets's calculate GCF of 9416,5390
| 2 | 9416, 5390 |
| 11 | 4708, 2695 |
| 428, 245 |
∴ So the GCF of the given numbers is 2 x 11 = 22
Greatest Common Factor of 9416,5390 By Matching Biggest Common Factor Method
Now, list down the factors of 9416
:1,2,4,8,11,22,44,88,107,214,428,856,1177,2354,4708,9416
Now, list down the factors of 5390
:1,2,5,7,10,11,14,22,35,49,55,70,77,98,110,154,245,385,490,539,770,1078,2695,5390
Greatest Common Factor
We found the factors 9416,5390 . The biggest common factor number is the GCF number.
So the greatest common factor 9416,5390 is 22.
Lets's calculate LCM of 349,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 142741
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/142741
Therefore, the GCF of Fractions 9416/349,5390/409 is 22/142741
Least Common Multiple of 349,409 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 349,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(349,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(349,409) x common factors =1 x 1 = 1
LCM(349,409) = ( 349 × 409 ) / 1
LCM(349,409) = 142741 / 1
LCM(349,409) = 142741
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FAQs on GCF of Fractions of 9416/349, 5390/409
1. What is the HCF of 9416,5390?
The HCF of 9416,5390 is 22
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 9416/349, 5390/409?
Answer: GCF of Numerators as per given numbers 9416/349, 5390/409 is
GCF of Numerators i.e. for 9416,5390 is 22
LCM of denominators i.e. for 349,409 is 142741.
Thus, GCF of Fractions is 22/142741.Finally, GCF of Fractions for 9416/349, 5390/409 is 22/142741.