GCF of 67/84, 73/972, 741/415
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 67/84, 73/972, 741/415 i.e 1/2823660 easily. The following is the detailed procedure to determine the greatest common factor of fractions 67/84, 73/972, 741/415.
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 67/84,73/972,741/415?
Given fractions are 67/84,73/972,741/415
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 67/84,73/972,741/415, numerators are 67,73,741
Denominators are 84,972,415
The GCF of 67,73,741 is 1 .
LCM of 84,972,415 is 2823660.
The greatest common factor of 67/84,73/972,741/415 = [GCF of 67,73,741]/[LCM of 84,972,415]= 1/2823660
Therefore, the GCF of 67/84,73/972,741/415 is 1/2823660.
To find the highest common factor of 67,73,741, we have to find the factors of both numbers and list the highest common factor.
The factors of 67 are 1, 67
The factors of 73 are 1, 73
The factors of 741 are 1, 3, 13, 19, 39, 57, 247, 741
The HCF of 67,73,741 is 1.
Lets's calculate GCF of 67,73,741
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 67,73,741 By Matching Biggest Common Factor Method
Now, list down the factors of 67
:1,67
Now, list down the factors of 73
:1,73
Now, list down the factors of 741
:1,3,13,19,39,57,247,741
Greatest Common Factor
We found the factors 67,73,741 . The biggest common factor number is the GCF number.
So the greatest common factor 67,73,741 is 1.
Lets's calculate LCM of 84,972,415
| 2 | 84, 972, 415 |
| 2 | 42, 486, 415 |
| 3 | 21, 243, 415 |
| 7, 81, 415 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 7 x 81 x 415 = 2823660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2823660
Therefore, the GCF of Fractions 67/84,73/972,741/415 is 1/2823660
Least Common Multiple of 84,972,415 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 84,972,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,972,415) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(84,972,415) x common factors =1 x 12 = 12
LCM(84,972,415) = ( 84 × 972 × 415 ) / 12
LCM(84,972,415) = 33883920 / 12
LCM(84,972,415) = 2823660
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FAQs on GCF of Fractions of 67/84, 73/972, 741/415
1. What is the HCF of 67,73,741?
The HCF of 67,73,741 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 67/84, 73/972, 741/415?
Answer: GCF of Numerators as per given numbers 67/84, 73/972, 741/415 is
GCF of Numerators i.e. for 67,73,741 is 1
LCM of denominators i.e. for 84,972,415 is 2823660.
Thus, GCF of Fractions is 1/2823660.Finally, GCF of Fractions for 67/84, 73/972, 741/415 is 1/2823660.