How many 3 digit numbers are divisible by 6 in all?

To find out how many 3-digit numbers are divisible by 6, we need to find the first and the last 3-digit numbers that are divisible by 6.

Step 1: Find the first 3-digit number divisible by 6 The first 3-digit number is 100, but it's not divisible by 6. The next number is 101, 102, and so on. The first 3-digit number divisible by 6 is 102.

Step 2: Find the last 3-digit number divisible by 6 The last 3-digit number is 999, but it's not divisible by 6. The previous number is 998, 997, and so on. The last 3-digit number divisible by 6 is 996.

Step 3: Count the numbers The numbers divisible by 6 form an arithmetic sequence with a common difference of 6, starting from 102 and ending at 996. The nth term of an arithmetic sequence can be found by the formula a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms.

So, 996 = 102 + (n-1)6. Solving this equation gives n = 150.

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