For a number to be divisible by 105 it must be divisible by 3, by 5 and by 7. So, divisibility by 3 requires all three of the following to be satisfied:
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a number can be divided by 2 evenly only if the number ends in the following numbers...0, 2, 4, 6, 8
a number can be divided by 3 evenly only if the sum of all the digits in the number is divisible by 3
a number can be divided by 4 if the numbers last two digits are divisible by 4
a number can be divided by 5 only if the number ends in the following... 0, 5
a number can be divided by 6 only if the number is divisible by two and three
a number can be divide by 7 only if the number can be divided by 7 (no way for 7)
a number can be divided by 8 only if the last two digits of the number is divisible by 8
a number can be divided by 9 only if the sum of all the digits in the number is divisible by 9
a number can be divided by ten only if it ends with the number zero
12
Three
Divisibility rules have been developed and refined by mathematicians over the centuries. It is difficult to attribute the invention of divisibility rules to a specific individual. However, some early rules can be traced back to ancient civilizations like the Egyptians, Babylonians, and Greeks. These rules were further expanded upon and formalized by various mathematicians throughout history.
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