How many 3-digit numbers are completely divisible 6 ?

Sure, here is the step by step solution:

Step 1: Identify the smallest 3-digit number divisible by 6. That is 102 (since 100 is not divisible by 6, the next number is 102).

Step 2: Identify the largest 3-digit number divisible by 6. That is 996 (since 1000 is not divisible by 6, the previous number is 996).

Step 3: The 3-digit numbers divisible by 6 form an arithmetic sequence with a common difference of 6, starting from 102 and ending at 996.

Step 4: Use the formula of the nth term of an arithmetic sequence, which is a + (n - 1) * d, where a is the first term, d is the common difference, and n is the number of terms.

Step 5: Substitute the values into the formula: 996 = 102 + (n - 1) * 6.

Step 6: Simplify the equation to find the value of n. The solution is n = 150.

So, there are 150 three-digit numbers that are completely divisible by 6.