7,271,000

2³ × 5³ × 11 × 661

Starting at 7,271,000, the Collatz iteration reaches 1 after 111 steps. The first transition is 3635500; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 5^3 × 11 × 661

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 18,588,960

Proper Divisor Sum 11,317,960

Digit Sum / Digital Root 17 (Root: 8)

Adjacent Primes #7270997 ← → #7271003

Radix Representation

Decimal	7271000
Binary	11011101111001001011000 (23 bits)
Octal	0o33571130
Hexadecimal	0x6EF258

Divisor Catalog (60 of 64)

1 2 4 5 8 10 11 20 22 25 40 44 50 55 88 100 110 125 200 220 250 275 440 500 550 661 1,000 1,100 1,322 1,375 2,200 2,644 2,750 3,305 5,288 5,500 6,610 7,271 11,000 13,220 14,542 16,525 26,440 29,084 33,050 36,355 58,168 66,100 72,710 82,625 132,200 145,420 165,250 181,775 290,840 330,500 363,550 661,000 727,100 908,875

Collatz Trajectory (111 steps to reach 1)

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

7,271,000 3,635,500 1,817,750 908,875 2,726,626 1,363,313 4,089,940 2,044,970 1,022,485 3,067,456 1,533,728 766,864 383,432 191,716 95,858 47,929 143,788 71,894 35,947 107,842 53,921 161,764 80,882 40,441 121,324 60,662 30,331 90,994 45,497 136,492 68,246 34,123 102,370 51,185 153,556 76,778 38,389 115,168 57,584 28,792 14,396 7,198 3,599 10,798 5,399 16,198 8,099 24,298 12,149 36,448 18,224 9,112 4,556 2,278 1,139 3,418 1,709 5,128 2,564 1,282

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