8,327,136

2⁵ × 3 × 127 × 683

8,327,136 factors as 2^5 × 3 × 127 × 683. Its 48 positive divisors give a proper-divisor sum of 13,735,968, so this integer is abundant. The Collatz stopping time is 212 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 127 × 683

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 22,063,104

Proper Divisor Sum 13,735,968

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #8327129 ← → #8327177

Radix Representation

Decimal	8327136
Binary	11111110000111111100000 (23 bits)
Octal	0o37607740
Hexadecimal	0x7F0FE0

Divisor Catalog (48)

1 2 3 4 6 8 12 16 24 32 48 96 127 254 381 508 683 762 1,016 1,366 1,524 2,032 2,049 2,732 3,048 4,064 4,098 5,464 6,096 8,196 10,928 12,192 16,392 21,856 32,784 65,568 86,741 173,482 260,223 346,964 520,446 693,928 1,040,892 1,387,856 2,081,784 2,775,712 4,163,568 8,327,136

Collatz Trajectory (212 steps to reach 1)

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

8,327,136 4,163,568 2,081,784 1,040,892 520,446 260,223 780,670 390,335 1,171,006 585,503 1,756,510 878,255 2,634,766 1,317,383 3,952,150 1,976,075 5,928,226 2,964,113 8,892,340 4,446,170 2,223,085 6,669,256 3,334,628 1,667,314 833,657 2,500,972 1,250,486 625,243 1,875,730 937,865 2,813,596 1,406,798 703,399 2,110,198 1,055,099 3,165,298 1,582,649 4,747,948 2,373,974 1,186,987 3,560,962 1,780,481 5,341,444 2,670,722 1,335,361 4,006,084 2,003,042 1,001,521 3,004,564 1,502,282 751,141 2,253,424 1,126,712 563,356 281,678 140,839 422,518 211,259 633,778 316,889

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