Number (or sum) of divisors from the prime factorisation

This type of question, asked 8 times: CDS 2 2018, CDS 2 2020, CDS 1 2022, CDS 2 2022, CDS 1 2023, CDS 2 2024, CDS 1 2025, CDS 1 2026. All 8 questions below, oldest first.

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Question 1
CDS 2 2018
7 $The number of divisors of the number 38808, exclusive of the divisors 1 and itself, is$
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Question 2
CDS 2 2020
19 $d(n)$
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Question 3
CDS 1 2022
35 $What is the number of divisors of 1000 (excluding 1 and 1000)?$
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Question 4
CDS 2 2022
21 $N = 12^6 \times 3^8 \times 5^3$
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Question 5
CDS 1 2023
22 $Consider the following statements in respect of all factors of 360 : 1. The number of factors is 24. 2. The sum of all factors is 1170. Which of the above statements is/are correct?$
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Question 6
CDS 2 2024
31 $N$
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Question 7
CDS 1 2025
48 $24^3 - 16^3 - 8^3$
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Question 8
CDS 1 2026
27 $What is the sum of all the divisors of 256 ?$
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Number (or sum) of divisors from the prime factorisation

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Question 8