563,430

2 × 3 × 5 × 7 × 2683

Starting at 563,430, the Collatz iteration reaches 1 after 84 steps. The first transition is 281715; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 7 × 2683

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,545,984

Proper Divisor Sum 982,554

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #563419 ← → #563447

Radix Representation

Decimal	563430
Binary	10001001100011100110 (20 bits)
Octal	0o2114346
Hexadecimal	0x898E6

Divisor Catalog (32)

1 2 3 5 6 7 10 14 15 21 30 35 42 70 105 210 2,683 5,366 8,049 13,415 16,098 18,781 26,830 37,562 40,245 56,343 80,490 93,905 112,686 187,810 281,715 563,430

Collatz Trajectory (84 steps to reach 1)

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

563,430 281,715 845,146 422,573 1,267,720 633,860 316,930 158,465 475,396 237,698 118,849 356,548 178,274 89,137 267,412 133,706 66,853 200,560 100,280 50,140 25,070 12,535 37,606 18,803 56,410 28,205 84,616 42,308 21,154 10,577 31,732 15,866 7,933 23,800 11,900 5,950 2,975 8,926 4,463 13,390 6,695 20,086 10,043 30,130 15,065 45,196 22,598 11,299 33,898 16,949 50,848 25,424 12,712 6,356 3,178 1,589 4,768 2,384 1,192 596

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