the number n can be expressed as the product of four prime numbers, exactly three of which are the same. how many different positive divisors does n have, inclu
Mathematics
itsliterallysaba
Question
the number n can be expressed as the product of four prime numbers, exactly three of which are the same. how many different positive divisors does n have, including n and 1 ?
1 Answer

1. User Answers sqdancefan
Answer:
8
Stepbystep explanation:
Give a prime factorization consisting of two primes, with one of them cubed, you want to know the number of positive integer divisors.
Divisors
The number of divisors is the product of the exponents of the prime factorization, each increased by 1.
Application
Your number is ...
n = (a^3)(b^1)
so the number of positive divisors is ...
(3+1)(1+1) = 4·2 = 8
The number n has 8 different positive divisors.
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Additional comment
The divisors are ...
1, a, b, a², ab, a³, a²b, a³b
Example: 24 = 2³·3 has divisors ...
1, 2, 3, 4, 6, 8, 12, 24