7,754,832

2⁴ × 3³ × 29 × 619

Starting at 7,754,832, the Collatz iteration reaches 1 after 54 steps. The first transition is 3877416; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 29 × 619

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 23,064,000

Proper Divisor Sum 15,309,168

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7754827 ← → #7754843

Radix Representation

Decimal	7754832
Binary	11101100101010001010000 (23 bits)
Octal	0o35452120
Hexadecimal	0x765450

Divisor Catalog (60 of 80)

1 2 3 4 6 8 9 12 16 18 24 27 29 36 48 54 58 72 87 108 116 144 174 216 232 261 348 432 464 522 619 696 783 1,044 1,238 1,392 1,566 1,857 2,088 2,476 3,132 3,714 4,176 4,952 5,571 6,264 7,428 9,904 11,142 12,528 14,856 16,713 17,951 22,284 29,712 33,426 35,902 44,568 53,853 66,852

Collatz Trajectory (54 steps to reach 1)

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

7,754,832 3,877,416 1,938,708 969,354 484,677 1,454,032 727,016 363,508 181,754 90,877 272,632 136,316 68,158 34,079 102,238 51,119 153,358 76,679 230,038 115,019 345,058 172,529 517,588 258,794 129,397 388,192 194,096 97,048 48,524 24,262 12,131 36,394 18,197 54,592 27,296 13,648 6,824 3,412 1,706 853 2,560 1,280 640 320 160 80 40 20 10 5 16 8 4 2 1

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