Divisibility Test for #3

First of all remember that:

Divisibility

When we say something like "a number is divisible by" means "when you divide one whole number by another whole number the result is a also a whole number"

  • 30 is divisible by 5, because 30 ÷ 5 = 6 (and 6 is a whole number).
  • 30 is NOT divisible by 8, because 30 ÷ 8 = 3.75 (and 3.75 is NOT a whole number).

 

Divisibility Test for 3
A whole number is divisible by 3 when the sum of each digit of it is also divisible by 3. Sometimes you must apply this rule again and again and finish when the sum is obviously an multiple of 3 like {3, 6, 9, 12, ...}.

 

Example 1

30 is divisible by 3, because 3 + 0 = 3 and 3 is divisible by 3.

♦ check! ♦
30 ÷ 3 = 10 (and 10 is a whole number).

 

Example 2

345,123 is divisible by 3, because 3 + 4 + 5 + 1 + 2 + 3 = 18.

If you are not sure if 18 is divisible by 3, repeat the process of adding its digits. See: 18: 1 + 8 = 9 and 9 is divisible by 3.

♦ check! ♦
345,123 ÷ 3 = 115,041 (and 115,041 is a whole number).

 

Example 3

347 is NOT divisible by 3, because 3 + 4 + 7 = 14. and 14 is NOT divisible by 3.

See: 1 + 4 = 5 and 5 is NOT divisible by 3.

♦ check! ♦
347÷ 3 = 115.6666... (and 115.6666... is NOT a whole number). ×

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Prof Cardy Meier

Mathematician of the Day


Lambert Adolphe Jacques Quetelet
2/22/1796
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