388,368

2⁴ × 3³ × 29 × 31

388,368 factors as 2^4 × 3^3 × 29 × 31. Its 80 positive divisors give a proper-divisor sum of 802,032, so this integer is abundant. The Collatz stopping time is 192 steps.

Prime Factor Structure

Factorization String 2^4 × 3^3 × 29 × 31

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 1,190,400

Proper Divisor Sum 802,032

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #388363 ← → #388369

Radix Representation

Decimal	388368
Binary	1011110110100010000 (19 bits)
Octal	0o1366420
Hexadecimal	0x5ED10

Divisor Catalog (60 of 80)

1 2 3 4 6 8 9 12 16 18 24 27 29 31 36 48 54 58 62 72 87 93 108 116 124 144 174 186 216 232 248 261 279 348 372 432 464 496 522 558 696 744 783 837 899 1,044 1,116 1,392 1,488 1,566 1,674 1,798 2,088 2,232 2,697 3,132 3,348 3,596 4,176 4,464

Collatz Trajectory (192 steps to reach 1)

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

388,368 194,184 97,092 48,546 24,273 72,820 36,410 18,205 54,616 27,308 13,654 6,827 20,482 10,241 30,724 15,362 7,681 23,044 11,522 5,761 17,284 8,642 4,321 12,964 6,482 3,241 9,724 4,862 2,431 7,294 3,647 10,942 5,471 16,414 8,207 24,622 12,311 36,934 18,467 55,402 27,701 83,104 41,552 20,776 10,388 5,194 2,597 7,792 3,896 1,948 974 487 1,462 731 2,194 1,097 3,292 1,646 823 2,470

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