407,888

2⁴ × 13 × 37 × 53

407,888 has the prime decomposition 2^4 × 13 × 37 × 53. Its 4 distinct prime factors produce 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 13 × 37 × 53

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 890,568

Proper Divisor Sum 482,680

Digit Sum / Digital Root 35 (Root: 8)

Adjacent Primes #407879 ← → #407893

Radix Representation

Decimal	407888
Binary	1100011100101010000 (19 bits)
Octal	0o1434520
Hexadecimal	0x63950

Divisor Catalog (40)

1 2 4 8 13 16 26 37 52 53 74 104 106 148 208 212 296 424 481 592 689 848 962 1,378 1,924 1,961 2,756 3,848 3,922 5,512 7,696 7,844 11,024 15,688 25,493 31,376 50,986 101,972 203,944 407,888

Collatz Trajectory (130 steps to reach 1)

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

407,888 203,944 101,972 50,986 25,493 76,480 38,240 19,120 9,560 4,780 2,390 1,195 3,586 1,793 5,380 2,690 1,345 4,036 2,018 1,009 3,028 1,514 757 2,272 1,136 568 284 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445

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