420,504

2³ × 3 × 7 × 2503

420,504 has the prime decomposition 2^3 × 3 × 7 × 2503. Its 4 distinct prime factors produce 32 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 7 × 2503

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,201,920

Proper Divisor Sum 781,416

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #420503 ← → #420521

Radix Representation

Decimal	420504
Binary	1100110101010011000 (19 bits)
Octal	0o1465230
Hexadecimal	0x66A98

Divisor Catalog (32)

1 2 3 4 6 7 8 12 14 21 24 28 42 56 84 168 2,503 5,006 7,509 10,012 15,018 17,521 20,024 30,036 35,042 52,563 60,072 70,084 105,126 140,168 210,252 420,504

Collatz Trajectory (104 steps to reach 1)

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

420,504 210,252 105,126 52,563 157,690 78,845 236,536 118,268 59,134 29,567 88,702 44,351 133,054 66,527 199,582 99,791 299,374 149,687 449,062 224,531 673,594 336,797 1,010,392 505,196 252,598 126,299 378,898 189,449 568,348 284,174 142,087 426,262 213,131 639,394 319,697 959,092 479,546 239,773 719,320 359,660 179,830 89,915 269,746 134,873 404,620 202,310 101,155 303,466 151,733 455,200 227,600 113,800 56,900 28,450 14,225 42,676 21,338 10,669 32,008 16,004

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