GCF of 675/81, 414/738
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 675/81, 414/738 i.e 9/6642 easily. The following is the detailed procedure to determine the greatest common factor of fractions 675/81, 414/738.
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 675/81,414/738?
Given fractions are 675/81,414/738
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 675/81,414/738, numerators are 675,414
Denominators are 81,738
The GCF of 675,414 is 9 .
LCM of 81,738 is 6642.
The greatest common factor of 675/81,414/738 = [GCF of 675,414]/[LCM of 81,738]= 9/6642
Therefore, the GCF of 675/81,414/738 is 9/6642.
To find the highest common factor of 675,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 675,414 is 9.
Lets's calculate GCF of 675,414
| 3 | 675, 414 |
| 3 | 225, 138 |
| 75, 46 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 675,414 By Matching Biggest Common Factor Method
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
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 675,414 . The biggest common factor number is the GCF number.
So the greatest common factor 675,414 is 9.
Lets's calculate LCM of 81,738
| 3 | 81, 738 |
| 3 | 27, 246 |
| 9, 82 |
∴ So the LCM of the given numbers is 3 x 3 x 9 x 82 = 6642
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/6642
Therefore, the GCF of Fractions 675/81,414/738 is 9/6642
Least Common Multiple of 81,738 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 81,738 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,738) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(81,738) x common factors =9 x 1 = 9
LCM(81,738) = ( 81 × 738 ) / 9
LCM(81,738) = 59778 / 9
LCM(81,738) = 6642
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FAQs on GCF of Fractions of 675/81, 414/738
1. What is the HCF of 675,414?
The HCF of 675,414 is 9
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 675/81, 414/738?
Answer: GCF of Numerators as per given numbers 675/81, 414/738 is
GCF of Numerators i.e. for 675,414 is 9
LCM of denominators i.e. for 81,738 is 6642.
Thus, GCF of Fractions is 9/6642.Finally, GCF of Fractions for 675/81, 414/738 is 9/6642.