42,768,012

2² × 3 × 7 × 19 × 127 × 211

42,768,012 factors as 2^2 × 3 × 7 × 19 × 127 × 211. Its 96 positive divisors give a proper-divisor sum of 78,801,268, so this integer is abundant. The Collatz stopping time is 67 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 7 × 19 × 127 × 211

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 121,569,280

Proper Divisor Sum 78,801,268

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #42767987 ← → #42768013

Radix Representation

Decimal	42768012
Binary	10100011001001011010001100 (26 bits)
Octal	0o243113214
Hexadecimal	0x28C968C

Divisor Catalog (60 of 96)

1 2 3 4 6 7 12 14 19 21 28 38 42 57 76 84 114 127 133 211 228 254 266 381 399 422 508 532 633 762 798 844 889 1,266 1,477 1,524 1,596 1,778 2,413 2,532 2,667 2,954 3,556 4,009 4,431 4,826 5,334 5,908 7,239 8,018 8,862 9,652 10,668 12,027 14,478 16,036 16,891 17,724 24,054 26,797

Collatz Trajectory (67 steps to reach 1)

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

42,768,012 21,384,006 10,692,003 32,076,010 16,038,005 48,114,016 24,057,008 12,028,504 6,014,252 3,007,126 1,503,563 4,510,690 2,255,345 6,766,036 3,383,018 1,691,509 5,074,528 2,537,264 1,268,632 634,316 317,158 158,579 475,738 237,869 713,608 356,804 178,402 89,201 267,604 133,802 66,901 200,704 100,352 50,176 25,088 12,544 6,272 3,136 1,568 784 392 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40

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