761,250

2 × 3 × 5⁴ × 7 × 29

Starting at 761,250, the Collatz iteration reaches 1 after 56 steps. The first transition is 380625; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 5^4 × 7 × 29

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 2,249,280

Proper Divisor Sum 1,488,030

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #761249 ← → #761251

Radix Representation

Decimal	761250
Binary	10111001110110100010 (20 bits)
Octal	0o2716642
Hexadecimal	0xB9DA2

Divisor Catalog (60 of 80)

1 2 3 5 6 7 10 14 15 21 25 29 30 35 42 50 58 70 75 87 105 125 145 150 174 175 203 210 250 290 350 375 406 435 525 609 625 725 750 870 875 1,015 1,050 1,218 1,250 1,450 1,750 1,875 2,030 2,175 2,625 3,045 3,625 3,750 4,350 4,375 5,075 5,250 6,090 7,250

Collatz Trajectory (56 steps to reach 1)

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

761,250 380,625 1,141,876 570,938 285,469 856,408 428,204 214,102 107,051 321,154 160,577 481,732 240,866 120,433 361,300 180,650 90,325 270,976 135,488 67,744 33,872 16,936 8,468 4,234 2,117 6,352 3,176 1,588 794 397 1,192 596 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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