GCF of 233/78, 414/343
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 233/78, 414/343 i.e 1/26754 easily. The following is the detailed procedure to determine the greatest common factor of fractions 233/78, 414/343.
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 233/78,414/343?
Given fractions are 233/78,414/343
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 233/78,414/343, numerators are 233,414
Denominators are 78,343
The GCF of 233,414 is 1 .
LCM of 78,343 is 26754.
The greatest common factor of 233/78,414/343 = [GCF of 233,414]/[LCM of 78,343]= 1/26754
Therefore, the GCF of 233/78,414/343 is 1/26754.
To find the highest common factor of 233,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 233 are 1, 233
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 233,414 is 1.
Lets's calculate GCF of 233,414
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 233,414 By Matching Biggest Common Factor Method
Now, list down the factors of 233
:1,233
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 233,414 . The biggest common factor number is the GCF number.
So the greatest common factor 233,414 is 1.
Lets's calculate LCM of 78,343
Given numbers has no common factors except 1. So, there LCM is their product i.e 26754
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/26754
Therefore, the GCF of Fractions 233/78,414/343 is 1/26754
Least Common Multiple of 78,343 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 78,343 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,343) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(78,343) x common factors =1 x 1 = 1
LCM(78,343) = ( 78 × 343 ) / 1
LCM(78,343) = 26754 / 1
LCM(78,343) = 26754
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FAQs on GCF of Fractions of 233/78, 414/343
1. What is the HCF of 233,414?
The HCF of 233,414 is 1
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 233/78, 414/343?
Answer: GCF of Numerators as per given numbers 233/78, 414/343 is
GCF of Numerators i.e. for 233,414 is 1
LCM of denominators i.e. for 78,343 is 26754.
Thus, GCF of Fractions is 1/26754.Finally, GCF of Fractions for 233/78, 414/343 is 1/26754.