There are 142 natural numbers divisible by 7 between 1 and 1000.
Here's how we arrive at that answer:
- Understanding the Problem: We need to find all numbers that can be divided by 7 without leaving a remainder, within the range of 1 to 1000.
- Finding the Largest Multiple: The largest number not exceeding 1000 that is divisible by 7 is 994, as 994 divided by 7 equals 142 (994 / 7 = 142).
- Counting the Multiples: This means there are 142 multiples of 7 between 1 and 1000 inclusive. This is because the multiples are 71, 72, 73... all the way up to 7142 which is 994.
Here's a breakdown in a table format:
| Starting Number | Ending Number | Divisor | Largest Multiple in Range | Number of Multiples |
|---|---|---|---|---|
| 1 | 1000 | 7 | 994 | 142 |
The reference confirms this, stating:
"The largest number not exceeding 1000 that is divisible by 7 is 994 (994/7 = 142). Thus there are 142 numbers not exceeding 1000 that are divisible by 7."
Therefore, there are exactly 142 natural numbers divisible by 7 between 1 and 1000.
