There are 43 numbers between 100 and 400 that are divisible by 7.
To determine this, we can find the smallest and largest multiples of 7 within the specified range and then calculate the total number of multiples.
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Smallest multiple of 7 greater than 100: Dividing 100 by 7 gives approximately 14.29. Therefore, the smallest multiple of 7 greater than 100 is 7 * 15 = 105.
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Largest multiple of 7 less than 400: Dividing 400 by 7 gives approximately 57.14. Therefore, the largest multiple of 7 less than 400 is 7 * 57 = 399.
Now we have an arithmetic progression (AP) with:
- First term (a) = 105
- Common difference (d) = 7
- Last term (l) = 399
To find the number of terms (n) in the AP, we can use the formula:
l = a + (n - 1)d
Substituting the values:
399 = 105 + (n - 1)7
294 = (n - 1)7
42 = n - 1
n = 43
Therefore, there are 43 numbers between 100 and 400 that are divisible by 7.
