413,728

2⁵ × 7 × 1847

413,728 has the prime decomposition 2^5 × 7 × 1847. Its 3 distinct prime factors produce 24 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 7 × 1847

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 931,392

Proper Divisor Sum 517,664

Digit Sum / Digital Root 25 (Root: 7)

Adjacent Primes #413719 ← → #413737

Radix Representation

Decimal	413728
Binary	1100101000000100000 (19 bits)
Octal	0o1450040
Hexadecimal	0x65020

Divisor Catalog (24)

1 2 4 7 8 14 16 28 32 56 112 224 1,847 3,694 7,388 12,929 14,776 25,858 29,552 51,716 59,104 103,432 206,864 413,728

Collatz Trajectory (143 steps to reach 1)

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

413,728 206,864 103,432 51,716 25,858 12,929 38,788 19,394 9,697 29,092 14,546 7,273 21,820 10,910 5,455 16,366 8,183 24,550 12,275 36,826 18,413 55,240 27,620 13,810 6,905 20,716 10,358 5,179 15,538 7,769 23,308 11,654 5,827 17,482 8,741 26,224 13,112 6,556 3,278 1,639 4,918 2,459 7,378 3,689 11,068 5,534 2,767 8,302 4,151 12,454 6,227 18,682 9,341 28,024 14,012 7,006 3,503 10,510 5,255 15,766

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