723,832

2³ × 173 × 523

723,832 factors as 2^3 × 173 × 523. Its 16 positive divisors give a proper-divisor sum of 643,808, so this integer is deficient. The Collatz stopping time is 105 steps.

Prime Factor Structure

Factorization String 2^3 × 173 × 523

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 1,367,640

Proper Divisor Sum 643,808

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #723829 ← → #723839

Radix Representation

Decimal	723832
Binary	10110000101101111000 (20 bits)
Octal	0o2605570
Hexadecimal	0xB0B78

Divisor Catalog (16)

1 2 4 8 173 346 523 692 1,046 1,384 2,092 4,184 90,479 180,958 361,916 723,832

Collatz Trajectory (105 steps to reach 1)

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

723,832 361,916 180,958 90,479 271,438 135,719 407,158 203,579 610,738 305,369 916,108 458,054 229,027 687,082 343,541 1,030,624 515,312 257,656 128,828 64,414 32,207 96,622 48,311 144,934 72,467 217,402 108,701 326,104 163,052 81,526 40,763 122,290 61,145 183,436 91,718 45,859 137,578 68,789 206,368 103,184 51,592 25,796 12,898 6,449 19,348 9,674 4,837 14,512 7,256 3,628 1,814 907 2,722 1,361 4,084 2,042 1,021 3,064 1,532 766

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