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Derek's phone number, 336 - 7624, has the property that the three-digit prefix, 336, equals the product of the last four digits, 7 times 6 times 2 times 4. How many seven-digit phone numbers beginning with 336 have this property?

 

I think its 84 fsr guys!

 
 Jun 8, 2021
 #1
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Prime factorization 336 is 2^4*3*7.

7 must be one of the digits. The last four digits must be: (7, 6, 4, 2), (7, 6, 8, 1), (7, 3, 8, 2), or (7, 3, 4, 4). Each of the first three produces 4!=24. 24*3=72. The last one produces 3!=12 posssibilities. 72+12=84, so you're correct. 

 

JP

 
 Jun 8, 2021

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