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Math Challenge I-B Number Theory

 
 
LinAmber的头像
Math Challenge I-B Number Theory
LinAmber - 2019年07月28日 Sunday 20:02
 

I do not know how to solve, in Chapter 4,

4.30.

 
ReynosoDavid的头像
Re: Math Challenge I-B Number Theory
ReynosoDavid - 2019年07月31日 Wednesday 22:41
 
With the same amount of money he can buy $4$ more roosters than the number of hens he can buy. How much do $4$ roosters cost? How much more does a hen cost than a rooster? Use this difference and the cost of the extra $4$ roosters to figure out how many hens he can buy. 
 
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LinAmber的头像
Re: Math Challenge I-B Number Theory
LinAmber - 2019年08月6日 Tuesday 16:36
 

I think you gave the wrong answer hints, because this is my problem:

Find all numbers that are multiples of 2,3,52,3,5 and have 1212 divisors.

 
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ReynosoDavid的头像
Re: Math Challenge I-B Number Theory
ReynosoDavid - 2019年08月7日 Wednesday 18:24
 

My apologies, it seems I was looking at chapter 5 of algebra.

Since we want the number to have exactly $12$ divisors, it is a multiple of $3$ distinct prime numbers,  and $12 = (1+1)(1+1)(2+1)$, the number must be of the form $2^a \times 3^b \times 5^c$, where two of the exponents are $1$ and one of the exponents is $2$.

What numbers can be obtain by doing this?

 
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