GCF of 34/90, 10/756, 287/405
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 34/90, 10/756, 287/405 i.e 1/11340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 34/90, 10/756, 287/405.
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 34/90,10/756,287/405?
Given fractions are 34/90,10/756,287/405
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 34/90,10/756,287/405, numerators are 34,10,287
Denominators are 90,756,405
The GCF of 34,10,287 is 1 .
LCM of 90,756,405 is 11340.
The greatest common factor of 34/90,10/756,287/405 = [GCF of 34,10,287]/[LCM of 90,756,405]= 1/11340
Therefore, the GCF of 34/90,10/756,287/405 is 1/11340.
To find the highest common factor of 34,10,287, we have to find the factors of both numbers and list the highest common factor.
The factors of 34 are 1, 2, 17, 34
The factors of 10 are 1, 2, 5, 10
The factors of 287 are 1, 7, 41, 287
The HCF of 34,10,287 is 1.
Lets's calculate GCF of 34,10,287
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 34,10,287 By Matching Biggest Common Factor Method
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 10
:1,2,5,10
Now, list down the factors of 287
:1,7,41,287
Greatest Common Factor
We found the factors 34,10,287 . The biggest common factor number is the GCF number.
So the greatest common factor 34,10,287 is 1.
Lets's calculate LCM of 90,756,405
| 2 | 90, 756, 405 |
| 3 | 45, 378, 405 |
| 3 | 15, 126, 135 |
| 3 | 5, 42, 45 |
| 5 | 5, 14, 15 |
| 1, 14, 3 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 5 x 1 x 14 x 3 = 11340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11340
Therefore, the GCF of Fractions 34/90,10/756,287/405 is 1/11340
Least Common Multiple of 90,756,405 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 90,756,405 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(90,756,405) = 9
common factors(in case of two or more numbers have common factors) = 270
GCF(90,756,405) x common factors =9 x 270 = 2430
LCM(90,756,405) = ( 90 × 756 × 405 ) / 2430
LCM(90,756,405) = 27556200 / 2430
LCM(90,756,405) = 11340
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FAQs on GCF of Fractions of 34/90, 10/756, 287/405
1. What is the HCF of 34,10,287?
The HCF of 34,10,287 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 34/90, 10/756, 287/405?
Answer: GCF of Numerators as per given numbers 34/90, 10/756, 287/405 is
GCF of Numerators i.e. for 34,10,287 is 1
LCM of denominators i.e. for 90,756,405 is 11340.
Thus, GCF of Fractions is 1/11340.Finally, GCF of Fractions for 34/90, 10/756, 287/405 is 1/11340.