398,412

2² × 3³ × 7 × 17 × 31

Prime Factor Structure

Factorization String 2^2 × 3^3 × 7 × 17 × 31

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 1,290,240

Proper Divisor Sum 891,828

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #398407 ← → #398417

Radix Representation

Decimal	398412
Binary	1100001010001001100 (19 bits)
Octal	0o1412114
Hexadecimal	0x6144C

Divisor Catalog (60 of 96)

1 2 3 4 6 7 9 12 14 17 18 21 27 28 31 34 36 42 51 54 62 63 68 84 93 102 108 119 124 126 153 186 189 204 217 238 252 279 306 357 372 378 434 459 476 527 558 612 651 714 756 837 868 918 1,054 1,071 1,116 1,302 1,428 1,581

Collatz Trajectory (99 steps to reach 1)

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

398,412 199,206 99,603 298,810 149,405 448,216 224,108 112,054 56,027 168,082 84,041 252,124 126,062 63,031 189,094 94,547 283,642 141,821 425,464 212,732 106,366 53,183 159,550 79,775 239,326 119,663 358,990 179,495 538,486 269,243 807,730 403,865 1,211,596 605,798 302,899 908,698 454,349 1,363,048 681,524 340,762 170,381 511,144 255,572 127,786 63,893 191,680 95,840 47,920 23,960 11,980 5,990 2,995 8,986 4,493 13,480 6,740 3,370 1,685 5,056 2,528

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