8,123,040

2⁵ × 3² × 5 × 5641

Starting at 8,123,040, the Collatz iteration reaches 1 after 155 steps. The first transition is 4061520; the starting value is even with 72 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 5641

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 27,724,788

Proper Divisor Sum 19,601,748

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #8122969 ← → #8123053

Radix Representation

Decimal	8123040
Binary	11110111111001010100000 (23 bits)
Octal	0o36771240
Hexadecimal	0x7BF2A0

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 60 72 80 90 96 120 144 160 180 240 288 360 480 720 1,440 5,641 11,282 16,923 22,564 28,205 33,846 45,128 50,769 56,410 67,692 84,615 90,256 101,538 112,820 135,384 169,230 180,512 203,076 225,640 253,845 270,768 338,460 406,152 451,280

Collatz Trajectory (155 steps to reach 1)

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

8,123,040 4,061,520 2,030,760 1,015,380 507,690 253,845 761,536 380,768 190,384 95,192 47,596 23,798 11,899 35,698 17,849 53,548 26,774 13,387 40,162 20,081 60,244 30,122 15,061 45,184 22,592 11,296 5,648 2,824 1,412 706 353 1,060 530 265 796 398 199 598 299 898 449 1,348 674 337 1,012 506 253 760 380 190 95 286 143 430 215 646 323 970 485 1,456

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