480,396

2² × 3 × 7² × 19 × 43

480,396 factors as 2^2 × 3 × 7^2 × 19 × 43. Its 72 positive divisors give a proper-divisor sum of 924,084, so this integer is abundant. The Collatz stopping time is 68 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7^2 × 19 × 43

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 1,404,480

Proper Divisor Sum 924,084

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #480391 ← → #480409

Radix Representation

Decimal	480396
Binary	1110101010010001100 (19 bits)
Octal	0o1652214
Hexadecimal	0x7548C

Divisor Catalog (60 of 72)

1 2 3 4 6 7 12 14 19 21 28 38 42 43 49 57 76 84 86 98 114 129 133 147 172 196 228 258 266 294 301 399 516 532 588 602 798 817 903 931 1,204 1,596 1,634 1,806 1,862 2,107 2,451 2,793 3,268 3,612 3,724 4,214 4,902 5,586 5,719 6,321 8,428 9,804 11,172 11,438

Collatz Trajectory (68 steps to reach 1)

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

480,396 240,198 120,099 360,298 180,149 540,448 270,224 135,112 67,556 33,778 16,889 50,668 25,334 12,667 38,002 19,001 57,004 28,502 14,251 42,754 21,377 64,132 32,066 16,033 48,100 24,050 12,025 36,076 18,038 9,019 27,058 13,529 40,588 20,294 10,147 30,442 15,221 45,664 22,832 11,416 5,708 2,854 1,427 4,282 2,141 6,424 3,212 1,606 803 2,410 1,205 3,616 1,808 904 452 226 113 340 170 85

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