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Determine the largest possible integer n such that 942! is divisible by 60^2.

 Sep 21, 2020
 #1
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942! = 2^935 * 3^467 * 5^233 * 7^155 * 11^92 * 13^77 * 17^58 * 19^51 * 23^41 * 29^33 * 31^30 * 37^25 * 41^22 * 43^21 * 47^20 * 53^17 * 59^15 * 61^15 * 67^14 * 71^13 * 73^12 * 79^11 * 83^11 * 89^10 * 97^9 * 101^9 * 103^9 * 107^8 * 109^8 * 113^8 * 127^7 * 131^7 * 137^6 * 139^6 * 149^6 * 151^6 * 157^6 * 163^5 * 167^5 * 173^5 * 179^5 * 181^5 * 191^4 * 193^4 * 197^4 * 199^4 * 211^4 * 223^4 * 227^4 * 229^4 * 233^4 * 239^3 * 241^3 * 251^3 * 257^3 * 263^3 * 269^3 * 271^3 * 277^3 * 281^3 * 283^3 * 293^3 * 307^3 * 311^3 * 313^3 * 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 * 487 * 491 * 499 * 503 * 509 * 521 * 523 * 541 * 547 * 557 * 563 * 569 * 571 * 577 * 587 * 593 * 599 * 601 * 607 * 613 * 617 * 619 * 631 * 641 * 643 * 647 * 653 * 659 * 661 * 673 * 677 * 683 * 691 * 701 * 709 * 719 * 727 * 733 * 739 * 743 * 751 * 757 * 761 * 769 * 773 * 787 * 797 * 809 * 811 * 821 * 823 * 827 * 829 * 839 * 853 * 857 * 859 * 863 * 877 * 881 * 883 * 887 * 907 * 911 * 919 * 929 * 937 * 941

 

I don't think you want 942! divisible by 60^2 BUT by 60^n !!!!!

The largest n = 233, so that 942! mod 60^233 = 0

 Sep 21, 2020
 #2
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What n?

To me your question makes no sense.

 

Maybe you do mean 60^n but maths is precise and you have written nonsense.

 Sep 26, 2020

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