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Formula
Find the number of divisors
Answer
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$$18 \times 2$$
$9$
Find the number of divisors
$\color{#FF6800}{ 18 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 }$
$ $ Do prime factorization $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 2 } \times 2 \times 3 ^ { 2 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \times 2 \times 3 ^ { 2 }$
$2 ^ { 1 } \times \color{#FF6800}{ 2 } \times 3 ^ { 2 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$2 ^ { 1 } \times \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \times 3 ^ { 2 }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \times \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } } \times 3 ^ { 2 }$
$ $ Add the exponent as the base is the same $ $
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \times 3 ^ { 2 }$
$2 ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \times 3 ^ { 2 }$
$ $ Add $ 1 $ and $ 1$
$2 ^ { \color{#FF6800}{ 2 } } \times 3 ^ { 2 }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } }$
$ $ Find the number of divisors using an exponent $ $
$\color{#FF6800}{ 9 }$
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