426,720

2⁵ × 3 × 5 × 7 × 127

426,720 has digital root 3. The neighboring primes are 426709 and 426731; its proper-divisor sum differs from the starting integer by 694,848.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 7 × 127

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 1,548,288

Proper Divisor Sum 1,121,568

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #426709 ← → #426731

Radix Representation

Decimal	426720
Binary	1101000001011100000 (19 bits)
Octal	0o1501340
Hexadecimal	0x682E0

Divisor Catalog (60 of 96)

1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 28 30 32 35 40 42 48 56 60 70 80 84 96 105 112 120 127 140 160 168 210 224 240 254 280 336 381 420 480 508 560 635 672 762 840 889 1,016 1,120 1,270 1,524 1,680 1,778 1,905 2,032

Collatz Trajectory (187 steps to reach 1)

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

426,720 213,360 106,680 53,340 26,670 13,335 40,006 20,003 60,010 30,005 90,016 45,008 22,504 11,252 5,626 2,813 8,440 4,220 2,110 1,055 3,166 1,583 4,750 2,375 7,126 3,563 10,690 5,345 16,036 8,018 4,009 12,028 6,014 3,007 9,022 4,511 13,534 6,767 20,302 10,151 30,454 15,227 45,682 22,841 68,524 34,262 17,131 51,394 25,697 77,092 38,546 19,273 57,820 28,910 14,455 43,366 21,683 65,050 32,525 97,576

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