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No calc please

 Jun 8, 2019

Best Answer 

 #1
avatar+99 
+1

To have exactly one factor that is prime, the number must be prime so the prime factorization is the number*1, because 1 is not prime.

The divisibility rule for 11 is to take the alternating sum and difference of the digits and if that is divisible by 11 so is the number.

Take the 4 digit palendrome ABBA and using this rule on it you get A-B+B-A=0, and 0 is divisible by 11 so every four digit palendrome is divisible by 11. No 4 digit palendromes have exactly one digit that is prime.

 

The only way to interperate this problm so that it has an answer is if you can repeat factors.

11*11*11 = 1331 is a four digit palendrome, and it also as only one unique prime factor.

 Jun 8, 2019
 #1
avatar+99 
+1
Best Answer

To have exactly one factor that is prime, the number must be prime so the prime factorization is the number*1, because 1 is not prime.

The divisibility rule for 11 is to take the alternating sum and difference of the digits and if that is divisible by 11 so is the number.

Take the 4 digit palendrome ABBA and using this rule on it you get A-B+B-A=0, and 0 is divisible by 11 so every four digit palendrome is divisible by 11. No 4 digit palendromes have exactly one digit that is prime.

 

The only way to interperate this problm so that it has an answer is if you can repeat factors.

11*11*11 = 1331 is a four digit palendrome, and it also as only one unique prime factor.

power27 Jun 8, 2019

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