398,448

2⁴ × 3² × 2767

398,448 factors as 2^4 × 3^2 × 2767. Its 30 positive divisors give a proper-divisor sum of 717,056, so this integer is abundant. The Collatz stopping time is 143 steps.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 2767

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 30

Divisor Sum (σ) 1,115,504

Proper Divisor Sum 717,056

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #398441 ← → #398459

Radix Representation

Decimal	398448
Binary	1100001010001110000 (19 bits)
Octal	0o1412160
Hexadecimal	0x61470

Divisor Catalog (30)

1 2 3 4 6 8 9 12 16 18 24 36 48 72 144 2,767 5,534 8,301 11,068 16,602 22,136 24,903 33,204 44,272 49,806 66,408 99,612 132,816 199,224 398,448

Collatz Trajectory (143 steps to reach 1)

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

398,448 199,224 99,612 49,806 24,903 74,710 37,355 112,066 56,033 168,100 84,050 42,025 126,076 63,038 31,519 94,558 47,279 141,838 70,919 212,758 106,379 319,138 159,569 478,708 239,354 119,677 359,032 179,516 89,758 44,879 134,638 67,319 201,958 100,979 302,938 151,469 454,408 227,204 113,602 56,801 170,404 85,202 42,601 127,804 63,902 31,951 95,854 47,927 143,782 71,891 215,674 107,837 323,512 161,756 80,878 40,439 121,318 60,659 181,978 90,989

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