Final answer:
To find the number of positive divisors of 19x29x59 that end in a 1, consider the prime factorization and the powers of the prime factors that result in a digit 1 when multiplied by the main prime factor.
Step-by-step explanation:
To find the number of positive divisors of 19x29x59 that end in a 1, we need to consider the prime factorization of the given number. The prime factorization of 19x29x59 is 19 * 29 * 59. A positive divisor of this number will have factors of 19, 29, and 59, but it may also have additional factors of 19, 29, or 59 raised to different powers. To end with a digit 1, we need to look at the powers of 19, 29, and 59 that result in a digit 1 when multiplied by the main prime factor.
For example, if we take the power of 19 as 1, the power of 29 as 1, and the power of 59 as 5, then the divisor will be 19^1 * 29^1 * 59^5. This will end with a digit 1. We can repeat this process for the other prime factors, considering different powers. By multiplying the possibilities for each prime factor, we can find all the positive divisors that end in a 1.
Therefore, the number of positive divisors of 19x29x59 that end in a 1 depends on the possible powers of 19, 29, and 59 and their combinations.