There are 1286 numbers between 1000 and 9999 that are divisible by 7.
To determine this, we first find the smallest and largest numbers in the range divisible by 7:
- The smallest number greater than 1000 that is divisible by 7 is 1001 (since 1000/7 ≈ 142.86, we round up to 143 * 7 = 1001).
- The largest number smaller than 9999 that is divisible by 7 is 9996 (since 9999/7 ≈ 1428.43, we round down to 1428 * 7 = 9996).
Now, we can think of the numbers divisible by 7 as forming an arithmetic sequence: 1001, 1008, 1015,... 9996.
We can use the formula for the nth term of an arithmetic sequence: an = a1 + (n - 1)d, where:
- an is the nth term (9996 in this case)
- a1 is the first term (1001)
- n is the number of terms (what we're solving for)
- d is the common difference (7)
Plugging in the values:
9996 = 1001 + (n - 1)7
8995 = (n - 1)7
1285 = n - 1
n = 1286
Therefore, there are 1286 numbers between 1000 and 9999 that are divisible by 7.
It is important to note that according to a reference, there are 343 integers from 1000 to 9999 that are divisible by 7 and also do not contain any 0, 1, or 2 digits. This is not the answer to the question about divisibility alone.
