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MATH / If a and b are positive integers such that gcd(a,b)=210, mathop{text{lcm}}[a,b]=210^3, and a<b, how many possible values are there for a?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

If aa and bb are positive integers such that gcd(a,b)=210\gcd(a,b)=210, $\mathop{\text{lcm}}[a,b]=210^3$, and a<ba<b, how many possible values are there for aa?
Plain-text mathematical notation (without MathML)
If a and b are positive integers such that gcd(a,b)=210, $\mathop{\text{lcm}}[a,b]=210^3$, and a<b, how many possible values are there for a?
Original LaTeX notation
If $a$ and $b$ are positive integers such that $\gcd(a,b)=210$, $\mathop{\text{lcm}}[a,b]=210^3$, and $a<b$, how many possible values are there for $a$?

level

Level 5

type

Number Theory

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Source and history

task_id
294bde9f-e105-568f-ab6e-1a1166aeccfa
task_key
number~5ftheory--test--294bde9f-e105-568f-ab6e-1a1166aeccfa
task_revision_id
1
config / split
number_theory / test

Official source

initial import