Find how many numbers with factors under a certain number.

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How many integers less than $4 000$ have exactly $4$ factors ?








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  • 5




    Think about prime factorisations.
    – Lord Shark the Unknown
    Aug 11 at 1:58






  • 5




    One type of number with four factors is a product of two distinct primes (e.g. $6$); another kind is the cube of a prime (e.g. $8$). Can you count those separately? Are there any other kinds?
    – G Tony Jacobs
    Aug 11 at 2:12










  • Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
    – Peter
    2 days ago










  • Look up divisor function to see how to compute the number of factors from the prime factorization. It comes up often on this site, so you could search here as well.
    – Ross Millikan
    2 days ago














up vote
3
down vote

favorite
1













How many integers less than $4 000$ have exactly $4$ factors ?








share|cite|improve this question


















  • 5




    Think about prime factorisations.
    – Lord Shark the Unknown
    Aug 11 at 1:58






  • 5




    One type of number with four factors is a product of two distinct primes (e.g. $6$); another kind is the cube of a prime (e.g. $8$). Can you count those separately? Are there any other kinds?
    – G Tony Jacobs
    Aug 11 at 2:12










  • Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
    – Peter
    2 days ago










  • Look up divisor function to see how to compute the number of factors from the prime factorization. It comes up often on this site, so you could search here as well.
    – Ross Millikan
    2 days ago












up vote
3
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How many integers less than $4 000$ have exactly $4$ factors ?








share|cite|improve this question















How many integers less than $4 000$ have exactly $4$ factors ?










share|cite|improve this question













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edited 2 days ago









Peter

45.2k939119




45.2k939119










asked Aug 11 at 1:58









A.Rin

296




296







  • 5




    Think about prime factorisations.
    – Lord Shark the Unknown
    Aug 11 at 1:58






  • 5




    One type of number with four factors is a product of two distinct primes (e.g. $6$); another kind is the cube of a prime (e.g. $8$). Can you count those separately? Are there any other kinds?
    – G Tony Jacobs
    Aug 11 at 2:12










  • Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
    – Peter
    2 days ago










  • Look up divisor function to see how to compute the number of factors from the prime factorization. It comes up often on this site, so you could search here as well.
    – Ross Millikan
    2 days ago












  • 5




    Think about prime factorisations.
    – Lord Shark the Unknown
    Aug 11 at 1:58






  • 5




    One type of number with four factors is a product of two distinct primes (e.g. $6$); another kind is the cube of a prime (e.g. $8$). Can you count those separately? Are there any other kinds?
    – G Tony Jacobs
    Aug 11 at 2:12










  • Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
    – Peter
    2 days ago










  • Look up divisor function to see how to compute the number of factors from the prime factorization. It comes up often on this site, so you could search here as well.
    – Ross Millikan
    2 days ago







5




5




Think about prime factorisations.
– Lord Shark the Unknown
Aug 11 at 1:58




Think about prime factorisations.
– Lord Shark the Unknown
Aug 11 at 1:58




5




5




One type of number with four factors is a product of two distinct primes (e.g. $6$); another kind is the cube of a prime (e.g. $8$). Can you count those separately? Are there any other kinds?
– G Tony Jacobs
Aug 11 at 2:12




One type of number with four factors is a product of two distinct primes (e.g. $6$); another kind is the cube of a prime (e.g. $8$). Can you count those separately? Are there any other kinds?
– G Tony Jacobs
Aug 11 at 2:12












Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
– Peter
2 days ago




Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
– Peter
2 days ago












Look up divisor function to see how to compute the number of factors from the prime factorization. It comes up often on this site, so you could search here as well.
– Ross Millikan
2 days ago




Look up divisor function to see how to compute the number of factors from the prime factorization. It comes up often on this site, so you could search here as well.
– Ross Millikan
2 days ago










1 Answer
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Any number can be written in the form of its prime factors, i.e. $$N=p_1^n_1p_2^n_2p_3^n_3ldots$$ Number of factors are given by $$(n_1+1)(n_2+1)(n_3+1)ldots$$ You are given the
number of factors are exactly $4$. Therefore number of possibilities are $2cdot 2$,$4cdot 1$ i.e. of the form $$N=p_1^1p_2^1$$ and $$N=p_3^3$$. Note that $17^3gt 4000, 13^3lt 4000$ . The first case would need some calculations or you can write a python script. Can you calculate now?






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    Any number can be written in the form of its prime factors, i.e. $$N=p_1^n_1p_2^n_2p_3^n_3ldots$$ Number of factors are given by $$(n_1+1)(n_2+1)(n_3+1)ldots$$ You are given the
    number of factors are exactly $4$. Therefore number of possibilities are $2cdot 2$,$4cdot 1$ i.e. of the form $$N=p_1^1p_2^1$$ and $$N=p_3^3$$. Note that $17^3gt 4000, 13^3lt 4000$ . The first case would need some calculations or you can write a python script. Can you calculate now?






    share|cite|improve this answer
























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      down vote













      Any number can be written in the form of its prime factors, i.e. $$N=p_1^n_1p_2^n_2p_3^n_3ldots$$ Number of factors are given by $$(n_1+1)(n_2+1)(n_3+1)ldots$$ You are given the
      number of factors are exactly $4$. Therefore number of possibilities are $2cdot 2$,$4cdot 1$ i.e. of the form $$N=p_1^1p_2^1$$ and $$N=p_3^3$$. Note that $17^3gt 4000, 13^3lt 4000$ . The first case would need some calculations or you can write a python script. Can you calculate now?






      share|cite|improve this answer






















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        up vote
        0
        down vote









        Any number can be written in the form of its prime factors, i.e. $$N=p_1^n_1p_2^n_2p_3^n_3ldots$$ Number of factors are given by $$(n_1+1)(n_2+1)(n_3+1)ldots$$ You are given the
        number of factors are exactly $4$. Therefore number of possibilities are $2cdot 2$,$4cdot 1$ i.e. of the form $$N=p_1^1p_2^1$$ and $$N=p_3^3$$. Note that $17^3gt 4000, 13^3lt 4000$ . The first case would need some calculations or you can write a python script. Can you calculate now?






        share|cite|improve this answer












        Any number can be written in the form of its prime factors, i.e. $$N=p_1^n_1p_2^n_2p_3^n_3ldots$$ Number of factors are given by $$(n_1+1)(n_2+1)(n_3+1)ldots$$ You are given the
        number of factors are exactly $4$. Therefore number of possibilities are $2cdot 2$,$4cdot 1$ i.e. of the form $$N=p_1^1p_2^1$$ and $$N=p_3^3$$. Note that $17^3gt 4000, 13^3lt 4000$ . The first case would need some calculations or you can write a python script. Can you calculate now?







        share|cite|improve this answer












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        share|cite|improve this answer










        answered 2 days ago









        prog_SAHIL

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