8,269,632

2⁶ × 3² × 7² × 293

Starting at 8,269,632, the Collatz iteration reaches 1 after 106 steps. The first transition is 4134816; the starting value is even with 126 positive divisors.

Prime Factor Structure

Factorization String 2^6 × 3^2 × 7^2 × 293

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 126

Divisor Sum (σ) 27,667,458

Proper Divisor Sum 19,397,826

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #8269619 ← → #8269663

Radix Representation

Decimal	8269632
Binary	11111100010111101000000 (23 bits)
Octal	0o37427500
Hexadecimal	0x7E2F40

Divisor Catalog (60 of 126)

1 2 3 4 6 7 8 9 12 14 16 18 21 24 28 32 36 42 48 49 56 63 64 72 84 96 98 112 126 144 147 168 192 196 224 252 288 293 294 336 392 441 448 504 576 586 588 672 784 879 882 1,008 1,172 1,176 1,344 1,568 1,758 1,764 2,016 2,051

Collatz Trajectory (106 steps to reach 1)

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

8,269,632 4,134,816 2,067,408 1,033,704 516,852 258,426 129,213 387,640 193,820 96,910 48,455 145,366 72,683 218,050 109,025 327,076 163,538 81,769 245,308 122,654 61,327 183,982 91,991 275,974 137,987 413,962 206,981 620,944 310,472 155,236 77,618 38,809 116,428 58,214 29,107 87,322 43,661 130,984 65,492 32,746 16,373 49,120 24,560 12,280 6,140 3,070 1,535 4,606 2,303 6,910 3,455 10,366 5,183 15,550 7,775 23,326 11,663 34,990 17,495 52,486

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