How many 3 digit numbers are divisible by 8?
The first such number is 104
the last such number is 992
992-104 = 888
888/8 = 111
but that would exclude the first number, so
there are 112 such numbers.
Now do the question in your previous post exactly the same way.
thank you
To find out how many three-digit numbers are divisible by 8, we can break the problem down into two parts:
1. Determine the range of three-digit numbers.
2. Count the number of numbers within that range that are divisible by 8.
Let's address each part in more detail:
1. Determine the range of three-digit numbers:
A three-digit number has three places: hundreds, tens, and units. The hundreds place cannot be zero, so it can take values from 1 to 9. The tens and units places can take values from 0 to 9, so they have 10 possible values each. Therefore, the total number of possible three-digit numbers is 9 * 10 * 10 = 900.
2. Count the number of numbers within that range that are divisible by 8:
To be divisible by 8, a number needs to satisfy the divisibility rule for 8, which states that the number formed by the last three digits of the given number must be divisible by 8.
For the unit place, there are 10 possible digits (0 to 9). Since 10 % 8 = 2, there are no numbers with a unit place that is divisible by 8.
For the tens and units place combined, there are 10 * 10 = 100 possible combinations of digits (00 to 99). Out of these, some combinations will form three-digit numbers that are divisible by 8. If we list all the combinations and check which ones are divisible by 8, we will find a pattern:
00, 08, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96.
As we can see, the pattern repeats every 12 combinations. So, for every set of 12 combinations, there will be one three-digit number divisible by 8.
The total number of sets of 12 is 100 / 12 = 8 with a remainder of 4. This means that there are 8 groups of 12 combinations and 4 additional combinations. Hence, there are 8 + 1 = 9 three-digit numbers divisible by 8.
Therefore, the answer is 9 three-digit numbers are divisible by 8.