Questions: Type a digit that makes this statement true. 521,29 is divisible by 6.

Transcript text: Type a digit that makes this statement true. $521,29 \square$ is divisible by 6.

Solution

Solution Steps

To determine the digit that makes the number $521,29 \square$ divisible by 6, we need to check two conditions:

The number must be divisible by 2 (i.e., the last digit must be even).
The number must be divisible by 3 (i.e., the sum of all digits must be divisible by 3).

Step 1: Check Divisibility by 2

To determine if $52129 \square$ is divisible by 6, we first need to check if it is divisible by 2. A number is divisible by 2 if its last digit is even. Therefore, the digit $\square$ must be one of $0, 2, 4, 6, 8$.

Step 2: Check Divisibility by 3

Next, we need to check if $52129 \square$ is divisible by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. Let's calculate the sum of the digits of $52129$:

\[ 5 + 2 + 1 + 2 + 9 = 19 \]

We need to find a digit $\square$ such that $19 + \square$ is divisible by 3. Testing the possible even digits:

$19 + 0 = 19$ (not divisible by 3)
$19 + 2 = 21$ (divisible by 3)
$19 + 4 = 23$ (not divisible by 3)
$19 + 6 = 25$ (not divisible by 3)
$19 + 8 = 27$ (divisible by 3)

Step 3: Verify the Digit

From the above calculations, the possible digits that make $52129 \square$ divisible by 3 are $2$ and $8$. Since both are even, they also satisfy the condition for divisibility by 2. Therefore, the digits that make $52129 \square$ divisible by 6 are $2$ and $8$.

Final Answer

$\boxed{2 \text{ or } 8}$

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