8,264,320

2⁷ × 5 × 37 × 349

Starting at 8,264,320, the Collatz iteration reaches 1 after 80 steps. The first transition is 4132160; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^7 × 5 × 37 × 349

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 20,349,000

Proper Divisor Sum 12,084,680

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #8264317 ← → #8264327

Radix Representation

Decimal	8264320
Binary	11111100001101010000000 (23 bits)
Octal	0o37415200
Hexadecimal	0x7E1A80

Divisor Catalog (60 of 64)

1 2 4 5 8 10 16 20 32 37 40 64 74 80 128 148 160 185 296 320 349 370 592 640 698 740 1,184 1,396 1,480 1,745 2,368 2,792 2,960 3,490 4,736 5,584 5,920 6,980 11,168 11,840 12,913 13,960 22,336 23,680 25,826 27,920 44,672 51,652 55,840 64,565 103,304 111,680 129,130 206,608 223,360 258,260 413,216 516,520 826,432 1,033,040

Collatz Trajectory (80 steps to reach 1)

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

8,264,320 4,132,160 2,066,080 1,033,040 516,520 258,260 129,130 64,565 193,696 96,848 48,424 24,212 12,106 6,053 18,160 9,080 4,540 2,270 1,135 3,406 1,703 5,110 2,555 7,666 3,833 11,500 5,750 2,875 8,626 4,313 12,940 6,470 3,235 9,706 4,853 14,560 7,280 3,640 1,820 910 455 1,366 683 2,050 1,025 3,076 1,538 769 2,308 1,154 577 1,732 866 433 1,300 650 325 976 488 244

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