706,752

2⁶ × 3³ × 409

706,752 factors as 2^6 × 3^3 × 409. Its 56 positive divisors give a proper-divisor sum of 1,376,048, so this integer is abundant. The Collatz stopping time is 136 steps.

Prime Factor Structure

Factorization String 2^6 × 3^3 × 409

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 56

Divisor Sum (σ) 2,082,800

Proper Divisor Sum 1,376,048

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #706751 ← → #706753

Radix Representation

Decimal	706752
Binary	10101100100011000000 (20 bits)
Octal	0o2544300
Hexadecimal	0xAC8C0

Divisor Catalog (56)

1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 96 108 144 192 216 288 409 432 576 818 864 1,227 1,636 1,728 2,454 3,272 3,681 4,908 6,544 7,362 9,816 11,043 13,088 14,724 19,632 22,086 26,176 29,448 39,264 44,172 58,896 78,528 88,344 117,792 176,688 235,584 353,376 706,752

Collatz Trajectory (136 steps to reach 1)

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

706,752 353,376 176,688 88,344 44,172 22,086 11,043 33,130 16,565 49,696 24,848 12,424 6,212 3,106 1,553 4,660 2,330 1,165 3,496 1,748 874 437 1,312 656 328 164 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790

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