336-7624 has the property that the 3-digit prefix 336= product of the last four digits. How many seven-digit numbers have the same property?

Derek’s phone number, 336-7624, has the property that the three-digit prefix, 336, equals the product of the last four digits, 7 أ— 6 أ— 2 أ— 4. How many seven-digit phone numbers
beginning with 336 have this property?
Answer is 84 phone numbers.

I could only find 72 such numbers. Can someone help?
7 must be at least one of the digits. Last 4 digits could be {7,6,4,2}, {7, 6,8,1}, {7,3,8,2}
Each set makes 24 possibilitles, hence a total of 24*3 = 72.
What 12 combination am I missing?

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1 Answer
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You missed {7,3,4,4}\{ 7 , 3, 4, 4 \}.

  

 

Ah, ah – thanks!
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2 days ago