There are 18 two-digit natural numbers that are divisible by 5.
To understand why, let's first define what we mean by "two-digit natural numbers." These are numbers from 10 to 99 inclusive. We are looking for numbers within this range that, when divided by 5, leave no remainder.
Finding the Numbers
We can identify these numbers by finding the smallest and largest two-digit multiples of 5:
- The smallest two-digit multiple of 5 is 10 (5 x 2).
- The largest two-digit multiple of 5 is 95 (5 x 19).
We need to find all multiples of 5 between 5 x 2 and 5 x 19. Essentially, we are counting the integers from 2 up to 19.
Calculating the Count
To find the total count, we can use this simple formula:
- Number of multiples = (Largest multiplier - Smallest multiplier) + 1
- Number of multiples = (19 - 2) + 1 = 17 + 1 = 18
List of Numbers
Here are all the two-digit natural numbers divisible by 5:
| Multiples of 5 |
|---|
| 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 |
As the reference states, "There exist 18 numbers of two digits that are divisible by 5."
