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The product of the digits of 3214 is 24. How many distinct four-digit positive integers are there such that the product of their digits equals 18?

 Oct 31, 2022
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There are no DISTINCT 4-digit integers whose product = 18! Why?

 

Because:18 =2 x 3 x 3 x 1 as follows:

 

1129 , 1136 , 1163 , 1192 , 1219 , 1233 , 1291 , 1316 , 1323 , 1332 , 1361 , 1613 , 1631 , 1912 , 1921 , 2119 , 2133 , 2191 , 2313 , 2331 , 2911 , 3116 , 3123 , 3132 , 3161 , 3213 , 3231 , 3312 , 3321 , 3611 , 6113 , 6131 , 6311 , 9112 , 9121 , 9211 , Total =  36 such 4-digit integers.

 

Note: Either 1 or 3 must be repeated because of prime factorization of 18 =1 x 2 x 3 x 3

 Oct 31, 2022

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