GCF of 900/65, 414/2898
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 900/65, 414/2898 i.e 18/188370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/65, 414/2898.
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 900/65,414/2898?
Given fractions are 900/65,414/2898
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 900/65,414/2898, numerators are 900,414
Denominators are 65,2898
The GCF of 900,414 is 18 .
LCM of 65,2898 is 188370.
The greatest common factor of 900/65,414/2898 = [GCF of 900,414]/[LCM of 65,2898]= 18/188370
Therefore, the GCF of 900/65,414/2898 is 18/188370.
To find the highest common factor of 900,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 900,414 is 18.
Lets's calculate GCF of 900,414
| 2 | 900, 414 |
| 3 | 450, 207 |
| 3 | 150, 69 |
| 50, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 900,414 By Matching Biggest Common Factor Method
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
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 900,414 . The biggest common factor number is the GCF number.
So the greatest common factor 900,414 is 18.
Lets's calculate LCM of 65,2898
Given numbers has no common factors except 1. So, there LCM is their product i.e 188370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/188370
Therefore, the GCF of Fractions 900/65,414/2898 is 18/188370
Least Common Multiple of 65,2898 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 65,2898 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(65,2898) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(65,2898) x common factors =1 x 1 = 1
LCM(65,2898) = ( 65 × 2898 ) / 1
LCM(65,2898) = 188370 / 1
LCM(65,2898) = 188370
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FAQs on GCF of Fractions of 900/65, 414/2898
1. What is the HCF of 900,414?
The HCF of 900,414 is 18
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 900/65, 414/2898?
Answer: GCF of Numerators as per given numbers 900/65, 414/2898 is
GCF of Numerators i.e. for 900,414 is 18
LCM of denominators i.e. for 65,2898 is 188370.
Thus, GCF of Fractions is 18/188370.Finally, GCF of Fractions for 900/65, 414/2898 is 18/188370.