There are 13 two-digit numbers that are multiples of 7.
To determine how many two-digit numbers are multiples of 7, we need to identify the smallest and largest two-digit multiples of 7 and then count how many there are between them. The smallest two-digit number is 10, and the largest is 99.
Let's find the first two-digit multiple of 7:
- 7 x 1 = 7 (one-digit number)
- 7 x 2 = 14 (first two-digit multiple)
Now, let's find the largest two-digit multiple of 7. We can do this by dividing 99 by 7 to find how many times 7 goes into 99:
- 99 / 7 = 14.14...
This tells us that 7 goes into 99 roughly 14 times. Therefore, the largest multiple of 7 that is less than 99 would be 7 x 14.
- 7 x 14 = 98 (the largest two-digit multiple of 7)
Now we have the first (14) and last (98) two-digit multiples of 7. To count how many there are, we can count how many multiples are between 7*2 and 7*14. We have the sequence 7*2, 7*3, ..., 7*14. This is the same as counting from 2 up to 14 which is equal to 14 - 2 + 1 = 13. Here's a list of those multiples:
| Multiple | Value |
|---|---|
| 7 x 2 | 14 |
| 7 x 3 | 21 |
| 7 x 4 | 28 |
| 7 x 5 | 35 |
| 7 x 6 | 42 |
| 7 x 7 | 49 |
| 7 x 8 | 56 |
| 7 x 9 | 63 |
| 7 x 10 | 70 |
| 7 x 11 | 77 |
| 7 x 12 | 84 |
| 7 x 13 | 91 |
| 7 x 14 | 98 |
Therefore, there are a total of **13** two-digit numbers that are multiples of 7.
