ow many 3 digit numbers are divisible by 6 in all?149150151166

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 Now, we have a sequence of numbers from 102 to 996 with a common difference of 6. The nth term of an arithmetic sequence can be found using the formula: a + (n - 1) * d, where a is the first term, d is the common difference, and n is the term number.

Let's set up the equation 102 + (n - 1) * 6 = 996 and solve for n:

996 - 102 = (n - 1) * 6 894 = (n - 1) * 6 n - 1 = 894 / 6 n - 1 = 149 n = 150

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