429,048

2³ × 3² × 59 × 101

Starting at 429,048, the Collatz iteration reaches 1 after 99 steps. The first transition is 214524; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 59 × 101

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,193,400

Proper Divisor Sum 764,352

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #429043 ← → #429083

Radix Representation

Decimal	429048
Binary	1101000101111111000 (19 bits)
Octal	0o1505770
Hexadecimal	0x68BF8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 59 72 101 118 177 202 236 303 354 404 472 531 606 708 808 909 1,062 1,212 1,416 1,818 2,124 2,424 3,636 4,248 5,959 7,272 11,918 17,877 23,836 35,754 47,672 53,631 71,508 107,262 143,016 214,524 429,048

Collatz Trajectory (99 steps to reach 1)

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

429,048 214,524 107,262 53,631 160,894 80,447 241,342 120,671 362,014 181,007 543,022 271,511 814,534 407,267 1,221,802 610,901 1,832,704 916,352 458,176 229,088 114,544 57,272 28,636 14,318 7,159 21,478 10,739 32,218 16,109 48,328 24,164 12,082 6,041 18,124 9,062 4,531 13,594 6,797 20,392 10,196 5,098 2,549 7,648 3,824 1,912 956 478 239 718 359 1,078 539 1,618 809 2,428 1,214 607 1,822 911 2,734

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