How many three-digit numbers are divisible by 6 in maths?

There are 150 three-digit numbers that are divisible by 6.

Understanding Divisibility by 6

A number is divisible by 6 if it is divisible by both 2 and 3. This means:

• The number must be even (divisible by 2).
• The sum of the digits of the number must be divisible by 3.

Calculating the Three-Digit Numbers Divisible by 6

• The smallest three-digit number is 100.
• The largest three-digit number is 999.

To find the number of multiples of 6 within this range, we can consider the following:

1. First Multiple: The first three-digit number divisible by 6 is 102 (since 102 / 6 = 17).
2. Last Multiple: The last three-digit number divisible by 6 is 996 (since 996 / 6 = 166).
3. Arithmetic Sequence: The multiples of 6 form an arithmetic sequence: 102, 108, 114, ..., 996.
4. Number of Terms: The number of terms in this arithmetic sequence can be found using the formula:

   Number of terms = (Last term - First term) / Common difference + 1
   Number of terms = (996 - 102) / 6 + 1
   Number of terms = 894 / 6 + 1
   Number of terms = 149 + 1
   Number of terms = 150

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

Reference:

The reference indicates that there are 150 such numbers divisible by 6. (09-Jan-2020)