GCF of 450/506, 8505/269
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 450/506, 8505/269 i.e 45/136114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 450/506, 8505/269.
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 450/506,8505/269?
Given fractions are 450/506,8505/269
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 450/506,8505/269, numerators are 450,8505
Denominators are 506,269
The GCF of 450,8505 is 45 .
LCM of 506,269 is 136114.
The greatest common factor of 450/506,8505/269 = [GCF of 450,8505]/[LCM of 506,269]= 45/136114
Therefore, the GCF of 450/506,8505/269 is 45/136114.
To find the highest common factor of 450,8505, we have to find the factors of both numbers and list the highest common factor.
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The factors of 8505 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 81, 105, 135, 189, 243, 315, 405, 567, 945, 1215, 1701, 2835, 8505
The HCF of 450,8505 is 45.
Lets's calculate GCF of 450,8505
| 3 | 450, 8505 |
| 3 | 150, 2835 |
| 5 | 50, 945 |
| 10, 189 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 450,8505 By Matching Biggest Common Factor Method
Now, list down the factors of 450
:1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450
Now, list down the factors of 8505
:1,3,5,7,9,15,21,27,35,45,63,81,105,135,189,243,315,405,567,945,1215,1701,2835,8505
Greatest Common Factor
We found the factors 450,8505 . The biggest common factor number is the GCF number.
So the greatest common factor 450,8505 is 45.
Lets's calculate LCM of 506,269
Given numbers has no common factors except 1. So, there LCM is their product i.e 136114
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/136114
Therefore, the GCF of Fractions 450/506,8505/269 is 45/136114
Least Common Multiple of 506,269 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 506,269 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(506,269) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(506,269) x common factors =1 x 1 = 1
LCM(506,269) = ( 506 × 269 ) / 1
LCM(506,269) = 136114 / 1
LCM(506,269) = 136114
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FAQs on GCF of Fractions of 450/506, 8505/269
1. What is the HCF of 450,8505?
The HCF of 450,8505 is 45
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 450/506, 8505/269?
Answer: GCF of Numerators as per given numbers 450/506, 8505/269 is
GCF of Numerators i.e. for 450,8505 is 45
LCM of denominators i.e. for 506,269 is 136114.
Thus, GCF of Fractions is 45/136114.Finally, GCF of Fractions for 450/506, 8505/269 is 45/136114.