3,648,000

2⁹ × 3 × 5³ × 19

Starting at 3,648,000, the Collatz iteration reaches 1 after 84 steps. The first transition is 1824000; the starting value is even with 160 positive divisors.

Prime Factor Structure

Factorization String 2^9 × 3 × 5^3 × 19

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 160

Divisor Sum (σ) 12,767,040

Proper Divisor Sum 9,119,040

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #3647989 ← → #3648031

Radix Representation

Decimal	3648000
Binary	1101111010101000000000 (22 bits)
Octal	0o15725000
Hexadecimal	0x37AA00

Divisor Catalog (60 of 160)

1 2 3 4 5 6 8 10 12 15 16 19 20 24 25 30 32 38 40 48 50 57 60 64 75 76 80 95 96 100 114 120 125 128 150 152 160 190 192 200 228 240 250 256 285 300 304 320 375 380 384 400 456 475 480 500 512 570 600 608

Collatz Trajectory (84 steps to reach 1)

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

3,648,000 1,824,000 912,000 456,000 228,000 114,000 57,000 28,500 14,250 7,125 21,376 10,688 5,344 2,672 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644 1,822 911 2,734 1,367 4,102 2,051 6,154 3,077 9,232 4,616 2,308 1,154 577 1,732 866 433 1,300 650

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