7,628,808

2³ × 3 × 11² × 37 × 71

Starting at 7,628,808, the Collatz iteration reaches 1 after 80 steps. The first transition is 3814404; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 11^2 × 37 × 71

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 21,833,280

Proper Divisor Sum 14,204,472

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #7628807 ← → #7628809

Radix Representation

Decimal	7628808
Binary	11101000110100000001000 (23 bits)
Octal	0o35064010
Hexadecimal	0x746808

Divisor Catalog (60 of 96)

1 2 3 4 6 8 11 12 22 24 33 37 44 66 71 74 88 111 121 132 142 148 213 222 242 264 284 296 363 407 426 444 484 568 726 781 814 852 888 968 1,221 1,452 1,562 1,628 1,704 2,343 2,442 2,627 2,904 3,124 3,256 4,477 4,686 4,884 5,254 6,248 7,881 8,591 8,954 9,372

Collatz Trajectory (80 steps to reach 1)

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

7,628,808 3,814,404 1,907,202 953,601 2,860,804 1,430,402 715,201 2,145,604 1,072,802 536,401 1,609,204 804,602 402,301 1,206,904 603,452 301,726 150,863 452,590 226,295 678,886 339,443 1,018,330 509,165 1,527,496 763,748 381,874 190,937 572,812 286,406 143,203 429,610 214,805 644,416 322,208 161,104 80,552 40,276 20,138 10,069 30,208 15,104 7,552 3,776 1,888 944 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38

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