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 ?
factoring integers
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up vote
3
down vote
favorite
How many integers less than $4 000$ have exactly $4$ factors ?
factoring integers
5
Think about prime factorisations.
â 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?
â G Tony Jacobs
Aug 11 at 2:12
Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
â 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.
â Ross Millikan
2 days ago
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
How many integers less than $4 000$ have exactly $4$ factors ?
factoring integers
How many integers less than $4 000$ have exactly $4$ factors ?
factoring integers
edited 2 days ago
Peter
45.2k939119
45.2k939119
asked Aug 11 at 1:58
A.Rin
296
296
5
Think about prime factorisations.
â 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?
â G Tony Jacobs
Aug 11 at 2:12
Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
â 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.
â Ross Millikan
2 days ago
add a comment |Â
5
Think about prime factorisations.
â 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?
â G Tony Jacobs
Aug 11 at 2:12
Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
â 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.
â Ross Millikan
2 days ago
5
5
Think about prime factorisations.
â Lord Shark the Unknown
Aug 11 at 1:58
Think about prime factorisations.
â 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?
â 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?
â G Tony Jacobs
Aug 11 at 2:12
Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
â Peter
2 days ago
Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
â 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.
â 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.
â Ross Millikan
2 days ago
add a comment |Â
1 Answer
1
active
oldest
votes
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?
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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?
add a comment |Â
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?
add a comment |Â
up vote
0
down vote
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?
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?
answered 2 days ago
prog_SAHIL
1,010218
1,010218
add a comment |Â
add a comment |Â
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5
Think about prime factorisations.
â 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?
â G Tony Jacobs
Aug 11 at 2:12
Prime factors ? Divisors ? Please be more precise what you mean with "factors" !
â 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.
â Ross Millikan
2 days ago