Statistics

Problem Statement for "ProductOfDigits"

Problem Statement

You are given an int N. Find the smallest positive integer X such that the product of its digits (in decimal notation) is equal to N. Return the number of digits in X, or return -1 if such a number does not exist.

Definition

Class:
ProductOfDigits
Method:
smallestNumber
Parameters:
int
Returns:
int
Method signature:
int smallestNumber(int N)
(be sure your method is public)

Constraints

  • N will be between 1 and 1,000,000,000, inclusive.

Examples

  1. 1

    Returns: 1

    Just take X = 1. It contains 1 digit.

  2. 10

    Returns: 2

    Here the smallest possible X is 25.

  3. 26

    Returns: -1

  4. 100

    Returns: 3

    The number 455 has 3 digits and the product of its digits is 4 * 5 * 5 = 100.

  5. 1024

    Returns: 4

  6. 65856

    Returns: 6

  7. 60761421

    Returns: 9

  8. 1171875

    Returns: 9

  9. 1959552

    Returns: 7

  10. 15116544

    Returns: 8

  11. 18750000

    Returns: 10

  12. 630262500

    Returns: 12

  13. 492075

    Returns: 7

  14. 9841500

    Returns: 9

  15. 11344725

    Returns: 9

  16. 790272000

    Returns: 11

  17. 9

    Returns: 1

  18. 32805000

    Returns: 9

  19. 94478400

    Returns: 9

  20. 68841472

    Returns: 9

  21. 357210

    Returns: 7

  22. 4900

    Returns: 5

  23. 2560000

    Returns: 8

  24. 243

    Returns: 3

  25. 35831808

    Returns: 9

  26. 567000000

    Returns: 11

  27. 38400000

    Returns: 10

  28. 2211840

    Returns: 8

  29. 122500000

    Returns: 11

  30. 214375000

    Returns: 11

  31. 214375000

    Returns: 11

  32. 10628820

    Returns: 8

  33. 76832

    Returns: 6

  34. 27648000

    Returns: 9

  35. 135056250

    Returns: 11

  36. 567000000

    Returns: 11

  37. 1843

    Returns: -1

  38. 4917248

    Returns: 8

  39. 8943

    Returns: -1

  40. 19845000

    Returns: 9

  41. 22680000

    Returns: 9

  42. 6730

    Returns: -1

  43. 15351

    Returns: -1

  44. 12582912

    Returns: 8

  45. 2016000

    Returns: 8

  46. 7260624

    Returns: 8

  47. 619573248

    Returns: 10

  48. 531562500

    Returns: 12

  49. 1008

    Returns: 4

  50. 8505

    Returns: 5

  51. 61740

    Returns: 6

  52. 53156250

    Returns: 10

  53. 15750

    Returns: 6

  54. 400

    Returns: 4

  55. 87516450

    Returns: 10

  56. 8388608

    Returns: 8

  57. 15116544

    Returns: 8

  58. 236027904

    Returns: 10

  59. 141750000

    Returns: 11

  60. 669615660

    Returns: 10

  61. 51438240

    Returns: 9

  62. 37632

    Returns: 6

  63. 5830

    Returns: -1

  64. 201326592

    Returns: 10

  65. 1518750

    Returns: 8

  66. 11524800

    Returns: 9

  67. 13608000

    Returns: 9

  68. 921984000

    Returns: 11

  69. 603979776

    Returns: 10

  70. 60025000

    Returns: 10

  71. 1151

    Returns: -1

  72. 7290

    Returns: 5

  73. 188956800

    Returns: 10

  74. 403200000

    Returns: 11

  75. 51030

    Returns: 6

  76. 340200

    Returns: 7

  77. 671088640

    Returns: 10

  78. 301181440

    Returns: 10

  79. 414720000

    Returns: 11

  80. 5184

    Returns: 4

  81. 2107392

    Returns: 8

  82. 108000

    Returns: 7

  83. 490000000

    Returns: 12

  84. 32592

    Returns: -1

  85. 245000

    Returns: 7

  86. 6360

    Returns: -1

  87. 1835008

    Returns: 7

  88. 31500

    Returns: 6

  89. 691200

    Returns: 7

  90. 82978560

    Returns: 10

  91. 5308416

    Returns: 8

  92. 3001250

    Returns: 9

  93. 1152

    Returns: 4

  94. 55112400

    Returns: 9

  95. 421654016

    Returns: 10

  96. 4816896

    Returns: 8

  97. 1102248

    Returns: 7

  98. 107163000

    Returns: 10

  99. 3789

    Returns: -1

  100. 393824025

    Returns: 10

  101. 210739200

    Returns: 10

  102. 1440600

    Returns: 8

  103. 540101520

    Returns: 10

  104. 6618

    Returns: -1

  105. 344207360

    Returns: 10

  106. 2520

    Returns: 4

  107. 864

    Returns: 4

  108. 906992640

    Returns: 10

  109. 10000000

    Returns: 10

  110. 6

    Returns: 1

  111. 999999991

    Returns: -1

  112. 304545100

    Returns: -1

  113. 999999999

    Returns: -1

  114. 999999937

    Returns: -1

  115. 900000000

    Returns: 12

  116. 1000000000

    Returns: 12

  117. 621

    Returns: -1

  118. 432

    Returns: 3

  119. 3888

    Returns: 4

  120. 3

    Returns: 1

  121. 2

    Returns: 1

  122. 479001599

    Returns: -1

  123. 38102400

    Returns: 9

  124. 48

    Returns: 2

  125. 67108864

    Returns: 9

  126. 15120

    Returns: 5

  127. 30

    Returns: 2

  128. 41928319

    Returns: -1

  129. 54

    Returns: 2

  130. 27

    Returns: 2

  131. 128

    Returns: 3

  132. 21

    Returns: 2

  133. 49

    Returns: 2

  134. 536870912

    Returns: 10

  135. 81

    Returns: 2

  136. 625

    Returns: 4

  137. 14

    Returns: 2

  138. 5

    Returns: 1

  139. 244140625

    Returns: 12

  140. 172872

    Returns: 6

  141. 48828125

    Returns: 11

  142. 8

    Returns: 1

  143. 463222882

    Returns: -1

  144. 23

    Returns: -1

  145. 7

    Returns: 1

  146. 512

    Returns: 3

  147. 999999986

    Returns: -1

  148. 1890

    Returns: 4

  149. 16

    Returns: 2

  150. 216

    Returns: 3

  151. 362880000

    Returns: 11

  152. 1048576

    Returns: 7

  153. 209952000

    Returns: 10

  154. 76204800

    Returns: 10

  155. 486

    Returns: 3

  156. 4

    Returns: 1

  157. 282475249

    Returns: 10

  158. 188888881

    Returns: -1

  159. 18

    Returns: 2

  160. 31

    Returns: -1

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