# Number System : Divisibility by 3

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Method 1 :** Take any number

Add together each digit in the number.

Check if the sum is divisible by 3.

If the sum is divisible by 3, then the original number is divisible by 3.

**Method 2 :** If a number is a multiplication of 3 consecutive numbers then that number is always divisible by 3. This is useful for when the number takes the form of [*n* × (*n* − 1) × (*n* + 1)]

**Method 3 : ** Subtract the quantity of the digits 2, 5 and 8 in the number from the quantity of the digits 1, 4 and 7 in the number. If the result is a multiple of 3, the original number is divisible by 3.

**Example**

**Method 1:**

- 576 (This is the original number)
- 5 + 7 + 6 = 18 (Add each individual digit together)
- 18 is divisible by 3 at which point we can stop. Alternatively we can continue using the same method if the number is still too large:
- 1 + 8 = 9 (Add each individual digit together)
- 9 ÷ 3 = 3 (Check to see if the number received is divisible by 3)
- 576 ÷ 3 = 192 (If the number obtained by using the rule is divisible by 3, then the whole number is divisible by 3)

**Method 2:**

- 720 (This is the original number)
- 8 × 9 × 10 = 720
- 720 ÷ 3 = 270

**Method 3: ** 16,499,205,854,376 has four of the digits 1, 4 and 7; four of the digits 2, 5 and 8; ∴ Since 4 − 4 = 0 is a multiple of 3, the number 16,499,205,854,376 is divisible by 3.

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