There are 45 two-digit even numbers that are divisible by 2.
Step-by-step explanation
The question essentially asks how many two-digit numbers are even. A number is even if it is divisible by 2. Therefore, the question is equivalent to 'How many two-digit numbers are divisible by 2'.
The reference provides a clear step-by-step calculation:
- There are 90 two-digit natural numbers. This is because two-digit numbers range from 10 to 99 (99-10 + 1 = 90).
- In a sequence of consecutive natural numbers, every other number is divisible by 2 (even).
- Since there are an even number of two-digit numbers, exactly half of them will be divisible by 2.
- Therefore, the number of two-digit numbers divisible by 2 is 90 / 2 = 45.
Examples
To further illustrate, here are some examples of two-digit even numbers:
- 10, 12, 14, 16 ... 98.
- Every other two-digit number is divisible by 2.
Why this is so
- Two-digit numbers range from 10 to 99.
- The first two-digit even number is 10, and the last is 98.
- The sequence of even numbers increases by 2.
- As the total count of two-digit numbers is 90 (an even number) exactly half are even, and hence divisible by 2.
Conclusion
Therefore, the number of two-digit even numbers (which are necessarily divisible by 2) is 45.
