请教这道题是如何解的,一定要有解析哟~
1个回答
2018-02-07
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Use the prime factorization to answer this question.
∵110=2×5×11=(1+1)×(4+1)×(10+1)
and 110n^3=2×5×11×n^3
∴n^3=p^3·q^9(p、q∈{2,5,11} and p≠q)
∴n=p·q^3
∴81n^4=3^4·p^4·q^12
∴(4+1)×(4+1)×(12+1)=325
so,the number 81n^4 have 325 positive integer divisors.
The answer is D
∵110=2×5×11=(1+1)×(4+1)×(10+1)
and 110n^3=2×5×11×n^3
∴n^3=p^3·q^9(p、q∈{2,5,11} and p≠q)
∴n=p·q^3
∴81n^4=3^4·p^4·q^12
∴(4+1)×(4+1)×(12+1)=325
so,the number 81n^4 have 325 positive integer divisors.
The answer is D
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Thank you so mach!
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