There are 77 integers between 60 and 600 that are divisible by 7.
To determine how many integers within a specific range are divisible by a given number, we can use a straightforward method. First, identify the smallest and largest numbers within the range that are divisible by the divisor. Then, apply a formula to find the count. According to the provided reference:
- The first number greater than 60 that is divisible by 7 is 63.
- The last number less than 600 that is divisible by 7 is 595.
- The problem then essentially involves finding how many multiples of 7 exist between 63 and 595, inclusive.
Here's the breakdown, using the information from the reference:
The smallest multiple of 7 in the given range is 63 (7 * 9). The largest multiple of 7 is 595 (7 * 85). To find the total count of multiples, consider the multiples of 7 are an arithmetic sequence, where the first term is 7*9 = 63 and the last term is 7*85=595. In other words, the problem comes down to determining how many numbers are between 9 and 85, inclusive. To solve this, we subtract 9 from 85 and add one: 85 - 9 + 1 = 77. This means there are 77 multiples of 7 between 60 and 600.
This is confirmed by the reference, which calculates the number of multiples of 7 in the range by dividing the difference (595 - 63 = 532) by the common divisor (7) and adding one, to include the first term: 532 / 7 = **76**, +1 equals 77. It also does 595/7 = **85** - 63/7 = **9**, 85-9=76, +1 =77
Therefore, there are 77 integers between 60 and 600 that are divisible by 7.
