562,104

2³ × 3² × 37 × 211

Starting at 562,104, the Collatz iteration reaches 1 after 177 steps. The first transition is 281052; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 37 × 211

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,570,920

Proper Divisor Sum 1,008,816

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #562103 ← → #562129

Radix Representation

Decimal	562104
Binary	10001001001110111000 (20 bits)
Octal	0o2111670
Hexadecimal	0x893B8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 37 72 74 111 148 211 222 296 333 422 444 633 666 844 888 1,266 1,332 1,688 1,899 2,532 2,664 3,798 5,064 7,596 7,807 15,192 15,614 23,421 31,228 46,842 62,456 70,263 93,684 140,526 187,368 281,052 562,104

Collatz Trajectory (177 steps to reach 1)

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

562,104 281,052 140,526 70,263 210,790 105,395 316,186 158,093 474,280 237,140 118,570 59,285 177,856 88,928 44,464 22,232 11,116 5,558 2,779 8,338 4,169 12,508 6,254 3,127 9,382 4,691 14,074 7,037 21,112 10,556 5,278 2,639 7,918 3,959 11,878 5,939 17,818 8,909 26,728 13,364 6,682 3,341 10,024 5,012 2,506 1,253 3,760 1,880 940 470 235 706 353 1,060 530 265 796 398 199 598

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