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How many numbers between $1$ and $6042$ (inclusive) are relatively prime to $3780$?

Hint: $53$ is a factor.

Here the problem is not the solution of the question, because I would simply remove all the multiples of prime factors of $3780$.

But I wonder what is the trick associated with the hint and using factor $53$.

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    Note: 53 is one of four prime factors of 6042: $6042=2\cdot3\cdot19\cdot53$. Note also that $3780 =2^2\cdot3^3\cdot5\cdot7$.2012-11-02
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    A misleading hint if ever there was one.2012-11-02
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    I'm wondering if somehow they expected you to use that $2*53 = 3*5*7+1$ and reduce the problem to a smaller count. But I'm not seeing directly how to do that.2012-11-02
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    Perhaps the hint is there just so you can finish the factoring. You could easily see the 2 and then the 3 and then you're left to figure out how to factor 1007. Not incredibly hard since you just need to try 2, 3, 5, 7, 11, 13, 17, and then 19. But, it is helpful.2012-11-02
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    How does factoring $6042$ help? It's $3780$ that you need to factor.2012-11-02
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    @RobertIsrael So, it's a bad hint. But, it's a much better explanation than assuming you're supposed to somehow use $53$ somewhere else in the problem. That's my point. The teacher did something stupid. It's not the first time a teacher has done it. It's not about some magic trick with the number 53. Why are we trying to find some explanation other than the obvious?2012-11-02

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