GCF of 469/75, 587/90, 576/32
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 469/75, 587/90, 576/32 i.e 1/7200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 469/75, 587/90, 576/32.
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 469/75,587/90,576/32?
Given fractions are 469/75,587/90,576/32
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 469/75,587/90,576/32, numerators are 469,587,576
Denominators are 75,90,32
The GCF of 469,587,576 is 1 .
LCM of 75,90,32 is 7200.
The greatest common factor of 469/75,587/90,576/32 = [GCF of 469,587,576]/[LCM of 75,90,32]= 1/7200
Therefore, the GCF of 469/75,587/90,576/32 is 1/7200.
To find the highest common factor of 469,587,576, we have to find the factors of both numbers and list the highest common factor.
The factors of 469 are 1, 7, 67, 469
The factors of 587 are 1, 587
The factors of 576 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
The HCF of 469,587,576 is 1.
Lets's calculate GCF of 469,587,576
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 469,587,576 By Matching Biggest Common Factor Method
Now, list down the factors of 469
:1,7,67,469
Now, list down the factors of 587
:1,587
Now, list down the factors of 576
:1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144,192,288,576
Greatest Common Factor
We found the factors 469,587,576 . The biggest common factor number is the GCF number.
So the greatest common factor 469,587,576 is 1.
Lets's calculate LCM of 75,90,32
| 2 | 75, 90, 32 |
| 3 | 75, 45, 16 |
| 5 | 25, 15, 16 |
| 5, 3, 16 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 5 x 3 x 16 = 7200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7200
Therefore, the GCF of Fractions 469/75,587/90,576/32 is 1/7200
Least Common Multiple of 75,90,32 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 75,90,32 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,90,32) = 1
common factors(in case of two or more numbers have common factors) = 30
GCF(75,90,32) x common factors =1 x 30 = 30
LCM(75,90,32) = ( 75 × 90 × 32 ) / 30
LCM(75,90,32) = 216000 / 30
LCM(75,90,32) = 7200
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FAQs on GCF of Fractions of 469/75, 587/90, 576/32
1. What is the HCF of 469,587,576?
The HCF of 469,587,576 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 469/75, 587/90, 576/32?
Answer: GCF of Numerators as per given numbers 469/75, 587/90, 576/32 is
GCF of Numerators i.e. for 469,587,576 is 1
LCM of denominators i.e. for 75,90,32 is 7200.
Thus, GCF of Fractions is 1/7200.Finally, GCF of Fractions for 469/75, 587/90, 576/32 is 1/7200.