7,537,800

2³ × 3 × 5² × 17 × 739

Starting at 7,537,800, the Collatz iteration reaches 1 after 155 steps. The first transition is 3768900; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 5^2 × 17 × 739

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 24,775,200

Proper Divisor Sum 17,237,400

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7537799 ← → #7537807

Radix Representation

Decimal	7537800
Binary	11100110000010010001000 (23 bits)
Octal	0o34602210
Hexadecimal	0x730488

Divisor Catalog (60 of 96)

1 2 3 4 5 6 8 10 12 15 17 20 24 25 30 34 40 50 51 60 68 75 85 100 102 120 136 150 170 200 204 255 300 340 408 425 510 600 680 739 850 1,020 1,275 1,478 1,700 2,040 2,217 2,550 2,956 3,400 3,695 4,434 5,100 5,912 7,390 8,868 10,200 11,085 12,563 14,780

Collatz Trajectory (155 steps to reach 1)

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

7,537,800 3,768,900 1,884,450 942,225 2,826,676 1,413,338 706,669 2,120,008 1,060,004 530,002 265,001 795,004 397,502 198,751 596,254 298,127 894,382 447,191 1,341,574 670,787 2,012,362 1,006,181 3,018,544 1,509,272 754,636 377,318 188,659 565,978 282,989 848,968 424,484 212,242 106,121 318,364 159,182 79,591 238,774 119,387 358,162 179,081 537,244 268,622 134,311 402,934 201,467 604,402 302,201 906,604 453,302 226,651 679,954 339,977 1,019,932 509,966 254,983 764,950 382,475 1,147,426 573,713 1,721,140

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