GCF of 675/470, 4800/4530
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 675/470, 4800/4530 i.e 75/212910 easily. The following is the detailed procedure to determine the greatest common factor of fractions 675/470, 4800/4530.
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 675/470,4800/4530?
Given fractions are 675/470,4800/4530
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 675/470,4800/4530, numerators are 675,4800
Denominators are 470,4530
The GCF of 675,4800 is 75 .
LCM of 470,4530 is 212910.
The greatest common factor of 675/470,4800/4530 = [GCF of 675,4800]/[LCM of 470,4530]= 75/212910
Therefore, the GCF of 675/470,4800/4530 is 75/212910.
To find the highest common factor of 675,4800, 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 4800 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 150, 160, 192, 200, 240, 300, 320, 400, 480, 600, 800, 960, 1200, 1600, 2400, 4800
The HCF of 675,4800 is 75.
Lets's calculate GCF of 675,4800
| 3 | 675, 4800 |
| 5 | 225, 1600 |
| 5 | 45, 320 |
| 9, 64 |
∴ So the GCF of the given numbers is 3 x 5 x 5 = 75
Greatest Common Factor of 675,4800 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 4800
:1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,32,40,48,50,60,64,75,80,96,100,120,150,160,192,200,240,300,320,400,480,600,800,960,1200,1600,2400,4800
Greatest Common Factor
We found the factors 675,4800 . The biggest common factor number is the GCF number.
So the greatest common factor 675,4800 is 75.
Lets's calculate LCM of 470,4530
| 2 | 470, 4530 |
| 5 | 235, 2265 |
| 47, 453 |
∴ So the LCM of the given numbers is 2 x 5 x 47 x 453 = 212910
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 75/212910
Therefore, the GCF of Fractions 675/470,4800/4530 is 75/212910
Least Common Multiple of 470,4530 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 470,4530 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(470,4530) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(470,4530) x common factors =10 x 1 = 10
LCM(470,4530) = ( 470 × 4530 ) / 10
LCM(470,4530) = 2129100 / 10
LCM(470,4530) = 212910
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FAQs on GCF of Fractions of 675/470, 4800/4530
1. What is the HCF of 675,4800?
The HCF of 675,4800 is 75
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 675/470, 4800/4530?
Answer: GCF of Numerators as per given numbers 675/470, 4800/4530 is
GCF of Numerators i.e. for 675,4800 is 75
LCM of denominators i.e. for 470,4530 is 212910.
Thus, GCF of Fractions is 75/212910.Finally, GCF of Fractions for 675/470, 4800/4530 is 75/212910.