7,306,376

2³ × 7 × 11 × 29 × 409

Starting at 7,306,376, the Collatz iteration reaches 1 after 248 steps. The first transition is 3653188; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 7 × 11 × 29 × 409

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 17,712,000

Proper Divisor Sum 10,405,624

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #7306373 ← → #7306381

Radix Representation

Decimal	7306376
Binary	11011110111110010001000 (23 bits)
Octal	0o33676210
Hexadecimal	0x6F7C88

Divisor Catalog (60 of 64)

1 2 4 7 8 11 14 22 28 29 44 56 58 77 88 116 154 203 232 308 319 406 409 616 638 812 818 1,276 1,624 1,636 2,233 2,552 2,863 3,272 4,466 4,499 5,726 8,932 8,998 11,452 11,861 17,864 17,996 22,904 23,722 31,493 35,992 47,444 62,986 83,027 94,888 125,972 130,471 166,054 251,944 260,942 332,108 521,884 664,216 913,297

Collatz Trajectory (248 steps to reach 1)

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

7,306,376 3,653,188 1,826,594 913,297 2,739,892 1,369,946 684,973 2,054,920 1,027,460 513,730 256,865 770,596 385,298 192,649 577,948 288,974 144,487 433,462 216,731 650,194 325,097 975,292 487,646 243,823 731,470 365,735 1,097,206 548,603 1,645,810 822,905 2,468,716 1,234,358 617,179 1,851,538 925,769 2,777,308 1,388,654 694,327 2,082,982 1,041,491 3,124,474 1,562,237 4,686,712 2,343,356 1,171,678 585,839 1,757,518 878,759 2,636,278 1,318,139 3,954,418 1,977,209 5,931,628 2,965,814 1,482,907 4,448,722 2,224,361 6,673,084 3,336,542 1,668,271

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