Question

A grocery store gave out to customers labeled . If a customer receives a coupon
with a prime factor of , they win a free turkey. How many winning coupons are there?

Answer 1

To determine how many winning coupons there are, we need to clarify a few key details from your question. First, it appears you might have meant to provide a specific number that represents the coupons, but it seems to be missing. In general, we can assume we are working with a range of coupon numbers, say, from 1 to \( n \).

Assuming you meant the coupons are labeled from 1 to \( n \) and that the winning coupons are those that have at least one prime factor, we can consider the following steps:

1. **Identify Prime Numbers**: First, let’s identify what prime factors are. A prime factor is a factor of a number that is a prime number, which means it is greater than 1 and has no positive divisors other than 1 and itself.

2. **Count Winning Coupons**: If we know the range of coupon numbers (from 1 to \( n \)), then we can find out how many of those have a prime factor.

Every integer greater than 1 has at least one prime factor. Therefore, if the coupons are numbered from 1 to \( n \), the only number that does not have a prime factor is 1 itself.

3. **Calculate**:

Thus, if your coupons are numbered from 1 to \( n \):
- The number of winning coupons (coupons with at least one prime factor) would be \( n - 1 \).

Please provide the specific number (or range) of coupons if you would like a more tailored or precise response!