Assignment-5-Q5
What is the smallest positive integer with exactly 2022 positive divisors?
2022 = 2 ∗ 3 ∗ 337 as it’s prime factorization
In order to find a number’s divisors
For example: 2m 3n 5p 7q ’s divisors = (m + 1)(n + 1)(p + 1)(q + 1)
so, 2a ∗ 3b ∗ 337c ’s divisors = (a + 1)(b + 1)(c + 1) and since the number of
divisors is given (2022), therefore the full equation is:
(a + 1)(b + 1)(c + 1) = 2022 = 2 ∗ 3 ∗ 337
Using the prime factorization of 2022, a, b, c can easily be found, which are
1, 2, 336 respectively. now as we are finding the smallest positive integer, the
number that has exactly 2022 positive divisors is:
2336 ∗ 32 ∗ 51
1