7,086,000

2⁴ × 3 × 5³ × 1181

Starting at 7,086,000, the Collatz iteration reaches 1 after 222 steps. The first transition is 3543000; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3 × 5^3 × 1181

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 22,864,608

Proper Divisor Sum 15,778,608

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #7085999 ← → #7086029

Radix Representation

Decimal	7086000
Binary	11011000001111110110000 (23 bits)
Octal	0o33017660
Hexadecimal	0x6C1FB0

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 40 48 50 60 75 80 100 120 125 150 200 240 250 300 375 400 500 600 750 1,000 1,181 1,200 1,500 2,000 2,362 3,000 3,543 4,724 5,905 6,000 7,086 9,448 11,810 14,172 17,715 18,896 23,620 28,344 29,525 35,430 47,240 56,688 59,050 70,860 88,575

Collatz Trajectory (222 steps to reach 1)

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

7,086,000 3,543,000 1,771,500 885,750 442,875 1,328,626 664,313 1,992,940 996,470 498,235 1,494,706 747,353 2,242,060 1,121,030 560,515 1,681,546 840,773 2,522,320 1,261,160 630,580 315,290 157,645 472,936 236,468 118,234 59,117 177,352 88,676 44,338 22,169 66,508 33,254 16,627 49,882 24,941 74,824 37,412 18,706 9,353 28,060 14,030 7,015 21,046 10,523 31,570 15,785 47,356 23,678 11,839 35,518 17,759 53,278 26,639 79,918 39,959 119,878 59,939 179,818 89,909 269,728

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