668,472

2³ × 3 × 7 × 23 × 173

668,472 factors as 2^3 × 3 × 7 × 23 × 173. Its 64 positive divisors give a proper-divisor sum of 1,336,008, so this integer is abundant. The Collatz stopping time is 185 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 7 × 23 × 173

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 2,004,480

Proper Divisor Sum 1,336,008

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #668471 ← → #668509

Radix Representation

Decimal	668472
Binary	10100011001100111000 (20 bits)
Octal	0o2431470
Hexadecimal	0xA3338

Divisor Catalog (60 of 64)

1 2 3 4 6 7 8 12 14 21 23 24 28 42 46 56 69 84 92 138 161 168 173 184 276 322 346 483 519 552 644 692 966 1,038 1,211 1,288 1,384 1,932 2,076 2,422 3,633 3,864 3,979 4,152 4,844 7,266 7,958 9,688 11,937 14,532 15,916 23,874 27,853 29,064 31,832 47,748 55,706 83,559 95,496 111,412

Collatz Trajectory (185 steps to reach 1)

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

668,472 334,236 167,118 83,559 250,678 125,339 376,018 188,009 564,028 282,014 141,007 423,022 211,511 634,534 317,267 951,802 475,901 1,427,704 713,852 356,926 178,463 535,390 267,695 803,086 401,543 1,204,630 602,315 1,806,946 903,473 2,710,420 1,355,210 677,605 2,032,816 1,016,408 508,204 254,102 127,051 381,154 190,577 571,732 285,866 142,933 428,800 214,400 107,200 53,600 26,800 13,400 6,700 3,350 1,675 5,026 2,513 7,540 3,770 1,885 5,656 2,828 1,414 707

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