There are 28 numbers between 1 and 200 that are divisible by 7.
Understanding the Solution
To find the number of multiples of 7 between 1 and 200, we can use the following approach:
- Identify the first multiple: The first multiple of 7 in this range is 7 itself (7 x 1 = 7).
- Identify the last multiple: The largest multiple of 7 less than or equal to 200 is 196 (7 x 28 = 196).
- Calculate the total number of multiples: The sequence of multiples forms an arithmetic progression with a common difference of 7. The number of terms in this arithmetic progression can be found using the formula:
(last term - first term) / common difference + 1. In this case, it's (196 - 7) / 7 + 1 = 28.
Therefore, there are 28 numbers between 1 and 200 that are divisible by 7. This is confirmed by multiple sources, including the provided reference stating that "7 is the first and 196 is the last number which is divisible by 7 out of the first 200 natural numbers. ∴ 28 numbers are divisible by 7."
Further Insights
- This problem demonstrates a basic application of arithmetic sequences and divisibility rules.
- Similar calculations can be used to determine the number of multiples of any number within a given range.
