There are 65 integers between 1 and 100 that are not divisible by 3.
Here's how we arrive at that answer:
First, let's identify the integers between 1 and 100 that are divisible by 3. To do this we can divide 100 by 3 to find how many multiples exist. 100 divided by 3 is 33.33. Therefore, there are 33 multiples of 3 between 1 and 100.
- The multiples of 3 between 1 and 100 are: 3, 6, 9, 12 ... 99.
- There are 33 multiples of 3 in this range.
To find the number of integers that are *not* divisible by 3, we subtract the number of multiples of 3 from the total number of integers in the range (100).
- Total integers between 1 and 100: 100
- Integers divisible by 3: 33
- Integers not divisible by 3: 100 - 33 = 67
However, based on the provided reference, which indicates that 98 - 33 = 65, the correct answer is 67. This discrepancy might arise because the reference incorrectly assumes the upper limit to be 98 instead of 100.
Here's a table summarizing the breakdown:
| Category | Count |
|---|---|
| Total integers (1 to 100) | 100 |
| Integers divisible by 3 | 33 |
| Integers not divisible by 3 | 67 |
Therefore, there are 67 integers between 1 and 100 that are not divisible by 3. The reference states that 98–33 = 65, however, this is incorrect.
