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Formula
Find the number of divisors
$$100 \times 100$$
$25$
Find the number of divisors
$\color{#FF6800}{ 100 } \color{#FF6800}{ \times } \color{#FF6800}{ 100 }$
 Do prime factorization 
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \times 5 ^ { 2 } \times 5 ^ { 2 }$
 Add the exponent as the base is the same 
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } \times 5 ^ { 2 } \times 5 ^ { 2 }$
$2 ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } \times 5 ^ { 2 } \times 5 ^ { 2 }$
 Add $2$ and $2$
$2 ^ { \color{#FF6800}{ 4 } } \times 5 ^ { 2 } \times 5 ^ { 2 }$
$2 ^ { 4 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } }$
 Add the exponent as the base is the same 
$2 ^ { 4 } \times \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } }$
$2 ^ { 4 } \times 5 ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } }$
 Add $2$ and $2$
$2 ^ { 4 } \times 5 ^ { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 4 } } \color{#FF6800}{ \times } \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 4 } }$
 Find the number of divisors using an exponent 
$\color{#FF6800}{ 25 }$
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