how many 3 digit numbers are divisible by 6 in all
How many 3 digit numbers are divisible by 6 in all?
Answer:
To find out how many three-digit numbers are divisible by 6, we need to first determine the range of three-digit numbers. The smallest three-digit number is 100, and the largest is 999. To check if a number is divisible by 6, we need to see if it is divisible by both 2 and 3.
- A number is divisible by 2 if its last digit is even. In this case, any three-digit number would have a divisible by 2 as all numbers have the last digit between 0 to 9.
- A number is divisible by 3 if the sum of its digits is divisible by 3. For three-digit numbers, we need to have 1, 2, or 3 as the first digit and an even number as the last digit for divisibility by both 2 and 3, so there are 4 possibilities for the middle digit because 1 + 2 + 3 + 4 = 10 which is divisible by 3.
Therefore, there are 3 (possible first digits) x 4 (possible middle digits) x 5 (possible last digits) = 60 three-digit numbers that are divisible by 6.