GCF of 208/107, 344/237
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 208/107, 344/237 i.e 8/25359 easily. The following is the detailed procedure to determine the greatest common factor of fractions 208/107, 344/237.
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 208/107,344/237?
Given fractions are 208/107,344/237
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 208/107,344/237, numerators are 208,344
Denominators are 107,237
The GCF of 208,344 is 8 .
LCM of 107,237 is 25359.
The greatest common factor of 208/107,344/237 = [GCF of 208,344]/[LCM of 107,237]= 8/25359
Therefore, the GCF of 208/107,344/237 is 8/25359.
To find the highest common factor of 208,344, we have to find the factors of both numbers and list the highest common factor.
The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208
The factors of 344 are 1, 2, 4, 8, 43, 86, 172, 344
The HCF of 208,344 is 8.
Lets's calculate GCF of 208,344
| 2 | 208, 344 |
| 2 | 104, 172 |
| 2 | 52, 86 |
| 26, 43 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 208,344 By Matching Biggest Common Factor Method
Now, list down the factors of 208
:1,2,4,8,13,16,26,52,104,208
Now, list down the factors of 344
:1,2,4,8,43,86,172,344
Greatest Common Factor
We found the factors 208,344 . The biggest common factor number is the GCF number.
So the greatest common factor 208,344 is 8.
Lets's calculate LCM of 107,237
Given numbers has no common factors except 1. So, there LCM is their product i.e 25359
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/25359
Therefore, the GCF of Fractions 208/107,344/237 is 8/25359
Least Common Multiple of 107,237 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 107,237 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(107,237) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(107,237) x common factors =1 x 1 = 1
LCM(107,237) = ( 107 × 237 ) / 1
LCM(107,237) = 25359 / 1
LCM(107,237) = 25359
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 208/107, 344/237
1. What is the HCF of 208,344?
The HCF of 208,344 is 8
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 208/107, 344/237?
Answer: GCF of Numerators as per given numbers 208/107, 344/237 is
GCF of Numerators i.e. for 208,344 is 8
LCM of denominators i.e. for 107,237 is 25359.
Thus, GCF of Fractions is 8/25359.Finally, GCF of Fractions for 208/107, 344/237 is 8/25359.