Question

determina la cantidad de divisores de A
A=35² x 42³ x 81

Answer 1

Respuesta:

576

Explicación:

$A = 35^{2} * 42^{3} * 81\\A = (7^{2} * 5^{2} ) (6^{3} *7^{3} )(3^{4} )\\A = 7^{2} *5^{2} *(2^{3} *3^{3} )*7^{3} *3^{4} \\A = 7^{2+3} *5^{2} *2^{3} *3^{3+4} \\A =7^{5} *5^{2} *2^{3} *3^{7} \\Numero de divisores=(5+1)*(2+1)*(3+1)*(7+1)\\Ndiv = 6*3*4*8\\Ndiv = 576$

Answer 2

Respuesta:

576

Explicación:

\begin{gathered}A = 35^{2} * 42^{3} * 81\\A = (7^{2} * 5^{2} ) (6^{3} *7^{3} )(3^{4} )\\A = 7^{2} *5^{2} *(2^{3} *3^{3} )*7^{3} *3^{4} \\A = 7^{2+3} *5^{2} *2^{3} *3^{3+4} \\A =7^{5} *5^{2} *2^{3} *3^{7} \\Numero de divisores=(5+1)*(2+1)*(3+1)*(7+1)\\Ndiv = 6*3*4*8\\Ndiv = 576\end{gathered}

A=35

2

∗42

3

∗81

A=(7

2

∗5

2

)(6

3

∗7

3

)(3

4

)

A=7

2

∗5

2

∗(2

3

∗3

3

)∗7

3

∗3

4

A=7

2+3

∗5

2

∗2

3

∗3

3+4

A=7

5

∗5

2

∗2

3

∗3

7

Numerodedivisores=(5+1)∗(2+1)∗(3+1)∗(7+1)

Ndiv=6∗3∗4∗8

Ndiv=576