A number is divisible (can be factored into two whole numbers (integers)):

Powers of two
by 2 if it is an even number                                Example: 173,592
     if it ends in an even number
     if it ends in 0, 2, 4, 6 or 8
     if the last digit is divisible by 2

by 4 if the last 2 digits are divisible by 4                Example: 3,520,716

by 8 if the last 3 digits are divisible by 8                Example: 2,739,560

by 2n if the last n digits are divisible by 2n
       Example: 9,873,248   The last 4 digits divide by 16   16=24

5s and 10s
by 5 if it ends in 0 or 5                                   Example: 1,928,375
     if the last digit is divisible by 5

by 10 if it ends in 0                                       Example: 98,730,480
      if the last 2 digits are divisible by 10

by 100 if it ends in 00                                     Example: 325,900
       if the last 3 digits are divisible by 100

by 10n if it ends in n 0s
       if the last n digits are divisible by 10n
       Example: 534,287,000   The last 3 digits divide by 1,000   1,000=103

by 20 if the last 2 digits are 00, 20, 40, 60 or 80         Example: 413,760
      if the last 2 digits are divisible by 20

by 25 if the last 2 digits are 00, 25, 50 or 75             Example: 456,975
      if the last 2 digits are divisible by 25

by 50 if the last 2 digits are 00 or 50                     Example: 673,250
      if the last 2 digits are divisible by 50

3s and 9s
by 3 if the sum of the digits is divisible by 3             Example: 310,245,672,918

     Shortcut:  Cross out all 0s, 3s, 6s and 9s and any 
       combination of digits which adds up to a multiple of 3
     If nothing is left

by 9 if the sum of the digits is divisible by 9             Example: 10,245,672,918

     Shortcut:  Cross out all 0s and 9s and any combination 
       of digits which adds up to a multiple of 9
     If nothing is left

Combinations
by 6 if it divides by 2 and 3                               Example: 4,503,912

by 12 if divides by 4 and 3                                 Example: 309,612

by 15 if it divides by 5 and 3                              Example: 12,045

by 18 if it divides by 2 and 9                              Example: 630,972

by 24 if it divides by 3 and 8                              Example: 2,019,276,024

by 30 if it divides by 10 and 3                             Example: 190,620

by 40 if it divides by 5 and 8                              Example: 63,951,480

by 45 if it divides by 5 and 9                              Example: 720,945

by 48 if it divides by 3 and 16                             Example: 81,696

by 60 if it divides by 5, 4 and 3                           Example: 13,821,780