472,787

7 × 17 × 29 × 137

Starting at 472,787, the Collatz iteration reaches 1 after 125 steps. The first transition is 1418362; the starting value is odd with 16 positive divisors.

Prime Factor Structure

Factorization String 7 × 17 × 29 × 137

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 596,160

Proper Divisor Sum 123,373

Digit Sum / Digital Root 35 (Root: 8)

Adjacent Primes #472763 ← → #472793

Radix Representation

Decimal	472787
Binary	1110011011011010011 (19 bits)
Octal	0o1633323
Hexadecimal	0x736D3

Divisor Catalog (16)

1 7 17 29 119 137 203 493 959 2,329 3,451 3,973 16,303 27,811 67,541 472,787

Collatz Trajectory (125 steps to reach 1)

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

472,787 1,418,362 709,181 2,127,544 1,063,772 531,886 265,943 797,830 398,915 1,196,746 598,373 1,795,120 897,560 448,780 224,390 112,195 336,586 168,293 504,880 252,440 126,220 63,110 31,555 94,666 47,333 142,000 71,000 35,500 17,750 8,875 26,626 13,313 39,940 19,970 9,985 29,956 14,978 7,489 22,468 11,234 5,617 16,852 8,426 4,213 12,640 6,320 3,160 1,580 790 395 1,186 593 1,780 890 445 1,336 668 334 167 502

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