8,460,420

2² × 3 × 5 × 37² × 103

Starting at 8,460,420, the Collatz iteration reaches 1 after 137 steps. The first transition is 4230210; the starting value is even with 72 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 37^2 × 103

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 24,583,104

Proper Divisor Sum 16,122,684

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #8460409 ← → #8460433

Radix Representation

Decimal	8460420
Binary	100000010001100010000100 (24 bits)
Octal	0o40214204
Hexadecimal	0x811884

Divisor Catalog (60 of 72)

1 2 3 4 5 6 10 12 15 20 30 37 60 74 103 111 148 185 206 222 309 370 412 444 515 555 618 740 1,030 1,110 1,236 1,369 1,545 2,060 2,220 2,738 3,090 3,811 4,107 5,476 6,180 6,845 7,622 8,214 11,433 13,690 15,244 16,428 19,055 20,535 22,866 27,380 38,110 41,070 45,732 57,165 76,220 82,140 114,330 141,007

Collatz Trajectory (137 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

8,460,420 4,230,210 2,115,105 6,345,316 3,172,658 1,586,329 4,758,988 2,379,494 1,189,747 3,569,242 1,784,621 5,353,864 2,676,932 1,338,466 669,233 2,007,700 1,003,850 501,925 1,505,776 752,888 376,444 188,222 94,111 282,334 141,167 423,502 211,751 635,254 317,627 952,882 476,441 1,429,324 714,662 357,331 1,071,994 535,997 1,607,992 803,996 401,998 200,999 602,998 301,499 904,498 452,249 1,356,748 678,374 339,187 1,017,562 508,781 1,526,344 763,172 381,586 190,793 572,380 286,190 143,095 429,286 214,643 643,930 321,965

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