7,189,100

2² × 5² × 29 × 37 × 67

Starting at 7,189,100, the Collatz iteration reaches 1 after 266 steps. The first transition is 3594550; the starting value is even with 72 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 29 × 37 × 67

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 16,821,840

Proper Divisor Sum 9,632,740

Digit Sum / Digital Root 26 (Root: 8)

Adjacent Primes #7189097 ← → #7189103

Radix Representation

Decimal	7189100
Binary	11011011011001001101100 (23 bits)
Octal	0o33331154
Hexadecimal	0x6DB26C

Divisor Catalog (60 of 72)

1 2 4 5 10 20 25 29 37 50 58 67 74 100 116 134 145 148 185 268 290 335 370 580 670 725 740 925 1,073 1,340 1,450 1,675 1,850 1,943 2,146 2,479 2,900 3,350 3,700 3,886 4,292 4,958 5,365 6,700 7,772 9,715 9,916 10,730 12,395 19,430 21,460 24,790 26,825 38,860 48,575 49,580 53,650 61,975 71,891 97,150

Collatz Trajectory (266 steps to reach 1)

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

7,189,100 3,594,550 1,797,275 5,391,826 2,695,913 8,087,740 4,043,870 2,021,935 6,065,806 3,032,903 9,098,710 4,549,355 13,648,066 6,824,033 20,472,100 10,236,050 5,118,025 15,354,076 7,677,038 3,838,519 11,515,558 5,757,779 17,273,338 8,636,669 25,910,008 12,955,004 6,477,502 3,238,751 9,716,254 4,858,127 14,574,382 7,287,191 21,861,574 10,930,787 32,792,362 16,396,181 49,188,544 24,594,272 12,297,136 6,148,568 3,074,284 1,537,142 768,571 2,305,714 1,152,857 3,458,572 1,729,286 864,643 2,593,930 1,296,965 3,890,896 1,945,448 972,724 486,362 243,181 729,544 364,772 182,386 91,193 273,580

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