A number is divisible by 7 if it can be written as 7 × k, where k is an integer. Since the set of integers Z is infinite, there are infinitely many multiples of 7 across all positive and negative integers.

A number is divisible by 7 if it can be written as 7 × k, where k is an integer. Since the set of integers Z is infinite, there are infinitely many multiples of 7 across all positive and negative integers.

How many numbers are divisible by 7

Answer: Infinitely many (unbounded). If a specific range is intended, such as two-digit numbers, there are 13; for three-digit numbers, there are 128.

Step-by-step solution

Step 1: Analyze the range of numbers

A number is divisible by 7 if it can be written as $7 \times k$ , where $k$ is an integer. Since the set of integers $\mathbb{Z}$ is infinite, there are infinitely many multiples of 7 across all positive and negative integers.

Step 2: State the general mathematical relationship

Because the problem does not specify a bounded interval (such as two-digit numbers, three-digit numbers, or numbers between 1 and 100), the system is mathematically unbounded. To find a finite count, a specific lower and upper boundary must be provided.

Step 3: Examine common textbook bounded interpretations

In standard curricula, this problem typically specifies a range such as two-digit numbers (where there are 13 numbers) or three-digit numbers (where there are 128 numbers). If a bounded range $[A, B]$ is provided, the count is computed as $\left\lfloor\frac{B}{7}\right\rfloor - \left\lfloor\frac{A-1}{7}\right\rfloor$ .

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