<h3>What is the greatest common factor for 60 and 45 ?</h3>
<em>The greatest common factor (GCF) is also known as greatest common divisor (GCD).</em>
<em>First we have to find the prime factorization of 60</em>
60 = 2² × 3 × 5
<em>Then we have to find the prime factorization of 45</em>
45 = 3² × 5
<em>Now we have to multiply the common factors to both numbers with a lower exponent</em>
GCF = 3 × 5 = 15
Answer : GCF(60,45) = 15
Hope this helps!
Using the greatest common factor, it is found that the greatest dimensions each tile can have is of 3 feet.
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- The widths of the walls are of <u>27 feet, 18 feet and 30 feet.</u>
- <u>The tiles must fit the width of each wall</u>, thus, the greatest dimension they can have is the greatest common factor of 27, 18 and 30.
To find their greatest common factor, these numbers must be factored into prime factors simultaneously, that is, only being divided by numbers of which all three are divisible, thus:
27 - 18 - 30|3
9 - 6 - 10
No numbers by which all of 9, 6 and 10 are divisible, thus, gcf(27,18,30) = 3 and the greatest dimensions each tile can have is of 3 feet.
A similar problem is given at brainly.com/question/6032811
Step-by-step explanation:
![= {( \frac{3 {x}^{2} y}{x {y}^{ - 1} } )}^{2} \times ( \frac{4 {x}^{ \frac{1}{2}} {y}^{ - 2} }{ \sqrt{27 {x}^{3} } } )](https://tex.z-dn.net/?f=%20%3D%20%20%7B%28%20%5Cfrac%7B3%20%7Bx%7D%5E%7B2%7D%20y%7D%7Bx%20%7By%7D%5E%7B%20-%201%7D%20%7D%20%29%7D%5E%7B2%7D%20%20%5Ctimes%20%28%20%5Cfrac%7B4%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%7D%20%7By%7D%5E%7B%20-%202%7D%20%20%7D%7B%20%5Csqrt%7B27%20%7Bx%7D%5E%7B3%7D%20%7D%20%7D%20%29)
![= {(3 {x}^{2 - 1} {y}^{1 - ( - 1)} )}^{2} \times (\frac{4 {x}^{ \frac{1}{2} } {y}^{ - 2} }{ {27}^{ \frac{1}{2} } {x}^{ \frac{3}{2} } } )](https://tex.z-dn.net/?f=%20%3D%20%20%7B%283%20%7Bx%7D%5E%7B2%20-%201%7D%20%20%7By%7D%5E%7B1%20-%20%28%20-%201%29%7D%20%29%7D%5E%7B2%7D%20%20%5Ctimes%20%20%28%5Cfrac%7B4%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%7By%7D%5E%7B%20-%202%7D%20%20%7D%7B%20%7B27%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20%7Bx%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%7D%20%29)
![= (3x {y}^{2} )^{2} \times ( \frac{4}{ {3}^{ \frac{3}{2} } } {x}^{ \frac{1}{2} - \frac{3}{2} } {y}^{ - 2} )](https://tex.z-dn.net/?f=%20%3D%20%283x%20%7By%7D%5E%7B2%7D%20%29%5E%7B2%7D%20%20%5Ctimes%20%20%28%20%5Cfrac%7B4%7D%7B%20%7B3%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%7D%20%7Bx%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20%20%7D%20%20%7By%7D%5E%7B%20-%202%7D%20%20%29)
![=( {3}^{2} {x}^{1 \times 2} {y}^{2 \times 2} ) \times ( \frac{4}{ {3}^{ \frac{3}{2} } } {x}^{ - 1} {y}^{ - 2} )](https://tex.z-dn.net/?f=%20%3D%28%20%20%7B3%7D%5E%7B2%7D%20%20%7Bx%7D%5E%7B1%20%5Ctimes%202%7D%20%20%7By%7D%5E%7B2%20%20%5Ctimes%202%7D%20%29%20%5Ctimes%20%28%20%5Cfrac%7B4%7D%7B%20%7B3%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%7D%20%20%7Bx%7D%5E%7B%20-%201%7D%20%20%7By%7D%5E%7B%20-%202%7D%20%29)
![= ( {3}^{2} {x}^{2} {y}^{4} ) \times ( \frac{4}{ {3}^{ \frac{3}{2} } x {y}^{2} } )](https://tex.z-dn.net/?f=%20%3D%20%28%20%7B3%7D%5E%7B2%7D%20%20%7Bx%7D%5E%7B2%7D%20%20%7By%7D%5E%7B4%7D%20%29%20%5Ctimes%20%28%20%5Cfrac%7B4%7D%7B%20%7B3%7D%5E%7B%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20x%20%7By%7D%5E%7B2%7D%20%7D%20%29)
![=4 \times {3}^{2 - \frac{3}{2} } {x}^{2 - 1} {y}^{4 - 2}](https://tex.z-dn.net/?f=%20%3D4%20%5Ctimes%20%20%20%7B3%7D%5E%7B2%20-%20%20%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%7Bx%7D%5E%7B2%20-%201%7D%20%20%7By%7D%5E%7B4%20-%202%7D%20)
![= 4 \times {3}^{ \frac{1}{2} } x {y}^{2}](https://tex.z-dn.net/?f=%20%3D%204%20%5Ctimes%20%20%7B3%7D%5E%7B%20%5Cfrac%7B1%7D%7B2%7D%20%7D%20x%20%7By%7D%5E%7B2%7D%20)
![= 4 \times \sqrt{3} xy](https://tex.z-dn.net/?f=%20%3D%204%20%5Ctimes%20%20%5Csqrt%7B3%7D%20xy)
![= 4xy \sqrt{3}](https://tex.z-dn.net/?f=%20%3D%204xy%20%5Csqrt%7B3%7D%20)
Anarchie ist die richtige Antwort