There are 37 integers between 200 and 500 that are divisible by eight.
Finding the Integers Divisible by 8
To determine how many integers within a given range are divisible by a specific number, you can follow these steps:
-
Identify the first multiple: Find the smallest number greater than 200 that is divisible by 8. In this case, it's 208 (since 200 divided by 8 is 25, then 25 8 = 200 and the next multiple is 26 8 = 208).
-
Identify the last multiple: Find the largest number less than 500 that is divisible by 8. In this case, it is 496 (since 500 divided by 8 is 62.5, so 62 * 8 = 496).
-
List the multiples: The multiples are thus 208, 216, 224, and so on, up to 496.
-
Arithmetic sequence: Recognize that these numbers form an arithmetic sequence with a common difference of 8.
-
Formula: To find the number of terms in an arithmetic sequence, use the formula:
n = ((last term - first term) / common difference) + 1
In this case:
n = ((496 - 208) / 8) + 1
n = (288 / 8) + 1
n = 36 + 1
n = 37
Therefore, there are 37 integers between 200 and 500 that are divisible by 8, which aligns with the given reference, "the no. of integers between 200 and 500 which are divisible by 8 are 37.".
