A number is divisible by 6 if it's divisible by both 2 and 3. Let's break down how to check for divisibility by 2 and 3:
Divisibility by 2:
A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8).
Divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Combining the Rules:
To determine if a number is divisible by 6, apply both rules:
- Check for divisibility by 2: Is the last digit even?
- Check for divisibility by 3: Add the digits. Is the sum divisible by 3?
If the answer to both questions is yes, then the number is divisible by 6.
Examples:
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4470:
- Ends in 0 (even), so it's divisible by 2.
- 4 + 4 + 7 + 0 = 15. 15 is divisible by 3 (3 x 5 = 15), so it's divisible by 3.
- Therefore, 4470 is divisible by 6.
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126:
- Ends in 6 (even), so it's divisible by 2.
- 1 + 2 + 6 = 9. 9 is divisible by 3 (3 x 3 = 9), so it's divisible by 3.
- Therefore, 126 is divisible by 6.
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105:
- Ends in 5 (odd), so it's not divisible by 2. Therefore, it's not divisible by 6. We don't even need to check divisibility by 3.
The provided YouTube video snippet also demonstrates this method, stating that a number ending in 0 is divisible by 2, and then checking the sum of the digits to determine divisibility by 3. Multiple sources (Cuemath, Vedantu, Smartick, etc.) confirm this process as the accurate method for determining divisibility by 6.
