There are exactly 43 integers between 200 and 500 that are divisible by 7.
Finding the Integers
To determine the number of integers between 200 and 500 divisible by 7, we need to:
-
Identify the First Multiple: The smallest integer greater than 200 that is divisible by 7 is 203 (since 200 / 7 ≈ 28.57 and 29 * 7 = 203).
-
Identify the Last Multiple: The largest integer less than 500 that is divisible by 7 is 497 (since 500 / 7 ≈ 71.42 and 71 * 7 = 497).
-
Use Arithmetic Progression: The integers divisible by 7 form an arithmetic progression: 203, 210, 217,... , 497. We know the first term (a=203), common difference (d=7) and the last term (l=497). The number of terms (n) in an arithmetic sequence is given by:
n = (l-a)/d + 1
Plugging in our values: n = (497 - 203)/7 + 1 = 294/7 + 1= 42+1=43.
Summary Table
| Detail | Value |
|---|---|
| First Multiple | 203 |
| Last Multiple | 497 |
| Common Difference | 7 |
| Total Integers | 43 |
Example
- The multiples of 7 are: 7, 14, 21, 28, 35... and so on
- Between 200 and 500, some of the multiples of 7 are: 203, 210, 217, 224, ... 490, 497
- As calculated, there are 43 multiples.
Therefore, as the reference states, there are 43 integers between 200 and 500 divisible by 7.
