A. What is the lowest number that has exactly 10 distinct positive factors?
B. Exactly 1,000 distinct positive factors?
C. Exactly 1,000,000 distinct positive factors?
Example: The distinct factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Thus 72 has 12 distinct factors.
A. 10 distinct factors
10 = 2* 5. The minimum pairs of primes are{2,5}
Thud thr smallest number satisfying this condition = 2^(5-1) * 3^(2-1) = 2^3*3^1=48
B. 1000 distinct factors
1000=2*2*2*5*5*5
Minimum sextuplet of primes:{2,3,5,7,11,13}
Thus the smallest number satisfying this condition is: 2^(5-1)*3^(5-1)*5^(5-1)*7*11*13
= 810,810,000
Edited on May 21, 2023, 10:49 pm
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