Find the greatest value of 'k' in the 6-digit number 6745k2 such that the number is divisible by 3.

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To check divisibility by 3, the sum of the digits of the number must be divisible by 3.

Given number: 6745k2
Sum of known digits = 6 + 7 + 4 + 5 + 2 = 24

Let the digit k be added to this sum:
Total sum = 24 + k

We want (24 + k) to be divisible by 3.

Since 24 is divisible by 3 (24 ÷ 3 = 8), k must also be divisible by 3 for the total sum to be divisible by 3.

Possible digits for k (0 to 9) divisible by 3 are: 0, 3, 6, 9.

The greatest value of k from these is 9.

Therefore, the greatest value of k such that the number is divisible by 3 is 9.

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