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Sunday, February 19, 2023

2023/006) Find 2 digit numbers that have exactly 5 factors

 If the umber is of the form \prod_{n=1}^{k}p_n^{q_n} then the number of factors = \prod_{n=1}^{k}(q_n+1)

Because 5 is prime the number must be of the form p^4 where p is prime

We have the number of digits =2 and we should find p such that 9 \lt p^4 \lt 100

The only number that satsfies the condition is n = 2 and n is a prime and 2^4= 16

So 16 is the only 2 digit number having 5 factors

 



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