How many 5 digit numbers are divisible by 8?

There are 11,250 five-digit numbers that are divisible by 8.

According to the provided reference, exactly 11,250 five-digit integers are divisible by 8. This can be determined by considering the properties of divisibility by 8.

Understanding Divisibility by 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8. When considering 5-digit numbers, we're looking at numbers from 10,000 to 99,999.

• The smallest 5-digit number is 10,000 and the largest is 99,999.
• The first 5-digit number divisible by 8 is 10,000 (10000 / 8 = 1250).
• The last 5-digit number divisible by 8 is 99,992 (99992 / 8 = 12499).

Calculating the Number of Divisible Numbers

We can treat this as an arithmetic sequence where the first term (a₁) is 10,000 and the last term (aₙ) is 99,992, with a common difference (d) of 8.

The formula to find the number of terms (n) in an arithmetic sequence is:

n = (aₙ - a₁) / d + 1

Plugging in our values:

n = (99,992 - 10,000) / 8 + 1
n = 89,992 / 8 + 1
n = 11,249 + 1
n = 11,250

Therefore, there are 11,250 five-digit numbers divisible by 8.