Final answer:
The factors of 1001 in prime factorization form are 1, 7, 11, 13, 77, 91, 143, and 1001. These factors are derived from the prime factorization of 1001, which is 7x11x13, considering each prime factor individually and in combinations.
Step-by-step explanation:
The student has been asked to list all the factors of the number 1001, given in prime factorization form as 7x11x13. In prime factorization form, the factors of 1001 would include the different combinations of the prime factors. To find all factors, we consider each prime factor individually and in combinations:
- 7 (just the prime factor 7)
- 11 (just the prime factor 11)
- 13 (just the prime factor 13)
- 7 × 11 = 77 (combination of prime factors)
- 7 × 13 = 91 (combination of prime factors)
- 11 × 13 = 143 (combination of prime factors)
- 7 × 11 × 13 = 1001 (all prime factors combined for the original number)
We also include 1, since 1 is a factor of every integer. Hence, the full list of factors of 1001 in prime factorization form would be: 1, 7, 11, 13, 77, 91, 143, and 1001.