GCF of 235/612, 7678/405
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 235/612, 7678/405 i.e 1/27540 easily. The following is the detailed procedure to determine the greatest common factor of fractions 235/612, 7678/405.
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 235/612,7678/405?
Given fractions are 235/612,7678/405
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 235/612,7678/405, numerators are 235,7678
Denominators are 612,405
The GCF of 235,7678 is 1 .
LCM of 612,405 is 27540.
The greatest common factor of 235/612,7678/405 = [GCF of 235,7678]/[LCM of 612,405]= 1/27540
Therefore, the GCF of 235/612,7678/405 is 1/27540.
To find the highest common factor of 235,7678, we have to find the factors of both numbers and list the highest common factor.
The factors of 235 are 1, 5, 47, 235
The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678
The HCF of 235,7678 is 1.
Lets's calculate GCF of 235,7678
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 235,7678 By Matching Biggest Common Factor Method
Now, list down the factors of 235
:1,5,47,235
Now, list down the factors of 7678
:1,2,11,22,349,698,3839,7678
Greatest Common Factor
We found the factors 235,7678 . The biggest common factor number is the GCF number.
So the greatest common factor 235,7678 is 1.
Lets's calculate LCM of 612,405
| 3 | 612, 405 |
| 3 | 204, 135 |
| 68, 45 |
∴ So the LCM of the given numbers is 3 x 3 x 68 x 45 = 27540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27540
Therefore, the GCF of Fractions 235/612,7678/405 is 1/27540
Least Common Multiple of 612,405 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 612,405 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(612,405) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(612,405) x common factors =9 x 1 = 9
LCM(612,405) = ( 612 × 405 ) / 9
LCM(612,405) = 247860 / 9
LCM(612,405) = 27540
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FAQs on GCF of Fractions of 235/612, 7678/405
1. What is the HCF of 235,7678?
The HCF of 235,7678 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 235/612, 7678/405?
Answer: GCF of Numerators as per given numbers 235/612, 7678/405 is
GCF of Numerators i.e. for 235,7678 is 1
LCM of denominators i.e. for 612,405 is 27540.
Thus, GCF of Fractions is 1/27540.Finally, GCF of Fractions for 235/612, 7678/405 is 1/27540.