How many ordered pairs (a, b) exist such that LCM of a and b is 23 57 1113 (a, b ∈ N)?2460283526452840
Question
How many ordered pairs (a, b) exist such that LCM of a and b is 23 57 1113 (a, b ∈ N)?2460283526452840
Solution
The given number is 23 57 1113.
First, we need to find the prime factorization of this number.
23 57 1113 = 3^2 * 7^2 * 11^3 * 13^3 * 17^2 * 19^2 * 23^2 * 29^2 * 31^2 * 37^2 * 41^2 * 43^2 * 47^2 * 53^2 * 59^2 * 61^2 * 67^2 * 71^2 * 73^2 * 79^2 * 83^2 * 89^2 * 97^2 * 101^2 * 103^2 * 107^2 * 109^2 * 113^2 * 127^2 * 131^2 * 137^2 * 139^2 * 149^2 * 151^2 * 157^2 * 163^2 * 167^2 * 173^2 * 179^2 * 181^2 * 191^2 * 193^2 * 197^2 * 199^2 * 211^2 * 223^2 * 227^2 * 229^2 * 233^2 * 239^2 * 241^2 * 251^2 * 257^2 * 263^2 * 269^2 * 271^2 * 277^2 * 281^2 * 283^2 * 293^2 * 307^2 * 311^2 * 313^2 * 317^2 * 331^2 * 337^2 * 347^2 * 349^2 * 353^2 * 359^2 * 367^2 * 373^2 * 379^2 * 383^2 * 389^2 * 397^2 * 401^2 * 409^2 * 419^2 * 421^2 * 431^2 * 433^2 * 439^2 * 443^2 * 449^2 * 457^2 * 461^2 * 463^2 * 467^2 * 479^2 * 487^2 * 491^2 * 499^2 * 503^2 * 509^2 * 521^2 * 523^2 * 541^2 * 547^2 * 557^2 * 563^2 * 569^2 * 571^2 * 577^2 * 587^2 * 593^2 * 599^2 * 601^2 * 607^2 * 613^2 * 617^2 * 619^2 * 631^2 * 641^2 * 643^2 * 647^2 * 653^2 * 659^2 * 661^2 * 673^2 * 677^2 * 683^2 * 691^2 * 701^2 * 709^2 * 719^2 * 727^2 * 733^2 * 739^2 * 743^2 * 751^2 * 757^2 * 761^2 * 769^2 * 773^2 * 787^2 * 797^2 * 809^2 * 811^2 * 821^2 * 823^2 * 827^2 * 829^2 * 839^2 * 853^2 * 857^2 * 859^2 * 863^2 * 877^2 * 881^2 * 883^2 * 887^2 * 907^2 * 911^2 * 919^2 * 929^2 * 937^2 * 941^2 * 947^2 * 953^2 * 967^2 * 971^2 * 977^2 *
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