GCF of 5338/106, 9228/116
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5338/106, 9228/116 i.e 2/6148 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5338/106, 9228/116.
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 5338/106,9228/116?
Given fractions are 5338/106,9228/116
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 5338/106,9228/116, numerators are 5338,9228
Denominators are 106,116
The GCF of 5338,9228 is 2 .
LCM of 106,116 is 6148.
The greatest common factor of 5338/106,9228/116 = [GCF of 5338,9228]/[LCM of 106,116]= 2/6148
Therefore, the GCF of 5338/106,9228/116 is 2/6148.
To find the highest common factor of 5338,9228, we have to find the factors of both numbers and list the highest common factor.
The factors of 5338 are 1, 2, 17, 34, 157, 314, 2669, 5338
The factors of 9228 are 1, 2, 3, 4, 6, 12, 769, 1538, 2307, 3076, 4614, 9228
The HCF of 5338,9228 is 2.
Lets's calculate GCF of 5338,9228
| 2 | 5338, 9228 |
| 2669, 4614 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 5338,9228 By Matching Biggest Common Factor Method
Now, list down the factors of 5338
:1,2,17,34,157,314,2669,5338
Now, list down the factors of 9228
:1,2,3,4,6,12,769,1538,2307,3076,4614,9228
Greatest Common Factor
We found the factors 5338,9228 . The biggest common factor number is the GCF number.
So the greatest common factor 5338,9228 is 2.
Lets's calculate LCM of 106,116
| 2 | 106, 116 |
| 53, 58 |
∴ So the LCM of the given numbers is 2 x 53 x 58 = 6148
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/6148
Therefore, the GCF of Fractions 5338/106,9228/116 is 2/6148
Least Common Multiple of 106,116 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 106,116 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,116) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(106,116) x common factors =2 x 1 = 2
LCM(106,116) = ( 106 × 116 ) / 2
LCM(106,116) = 12296 / 2
LCM(106,116) = 6148
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FAQs on GCF of Fractions of 5338/106, 9228/116
1. What is the HCF of 5338,9228?
The HCF of 5338,9228 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 5338/106, 9228/116?
Answer: GCF of Numerators as per given numbers 5338/106, 9228/116 is
GCF of Numerators i.e. for 5338,9228 is 2
LCM of denominators i.e. for 106,116 is 6148.
Thus, GCF of Fractions is 2/6148.Finally, GCF of Fractions for 5338/106, 9228/116 is 2/6148.