429,030

2 × 3³ × 5 × 7 × 227

429,030 factors as 2 × 3^3 × 5 × 7 × 227. Its 64 positive divisors give a proper-divisor sum of 884,250, so this integer is abundant. The Collatz stopping time is 99 steps.

Prime Factor Structure

Factorization String 2 × 3^3 × 5 × 7 × 227

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 1,313,280

Proper Divisor Sum 884,250

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #429017 ← → #429043

Radix Representation

Decimal	429030
Binary	1101000101111100110 (19 bits)
Octal	0o1505746
Hexadecimal	0x68BE6

Divisor Catalog (60 of 64)

1 2 3 5 6 7 9 10 14 15 18 21 27 30 35 42 45 54 63 70 90 105 126 135 189 210 227 270 315 378 454 630 681 945 1,135 1,362 1,589 1,890 2,043 2,270 3,178 3,405 4,086 4,767 6,129 6,810 7,945 9,534 10,215 12,258 14,301 15,890 20,430 23,835 28,602 30,645 42,903 47,670 61,290 71,505

Collatz Trajectory (99 steps to reach 1)

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

429,030 214,515 643,546 321,773 965,320 482,660 241,330 120,665 361,996 180,998 90,499 271,498 135,749 407,248 203,624 101,812 50,906 25,453 76,360 38,180 19,090 9,545 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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