λ
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Atlas › Integer Profiles › Node 42,831,200

42,831,200

25 × 52 × 37 × 1447
Abundant Even Composite

42,831,200 factors as 2^5 × 5^2 × 37 × 1447. Its 72 positive divisors give a proper-divisor sum of 64,630,672, so this integer is abundant. The Collatz stopping time is 204 steps.

Prime Factor Structure

Factorization String 2^5 × 5^2 × 37 × 1447
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 107,461,872
Proper Divisor Sum 64,630,672
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #42831197 ← → #42831203

Radix Representation

Decimal 42831200
Binary 10100011011000110101100000 (26 bits)
Octal 0o243306540
Hexadecimal 0x28D8D60

Divisor Catalog (60 of 72)

1 2 4 5 8 10 16 20 25 32 37 40 50 74 80 100 148 160 185 200 296 370 400 592 740 800 925 1,184 1,447 1,480 1,850 2,894 2,960 3,700 5,788 5,920 7,235 7,400 11,576 14,470 14,800 23,152 28,940 29,600 36,175 46,304 53,539 57,880 72,350 107,078 115,760 144,700 214,156 231,520 267,695 289,400 428,312 535,390 578,800 856,624

Collatz Trajectory (204 steps to reach 1)

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

42,831,200 21,415,600 10,707,800 5,353,900 2,676,950 1,338,475 4,015,426 2,007,713 6,023,140 3,011,570 1,505,785 4,517,356 2,258,678 1,129,339 3,388,018 1,694,009 5,082,028 2,541,014 1,270,507 3,811,522 1,905,761 5,717,284 2,858,642 1,429,321 4,287,964 2,143,982 1,071,991 3,215,974 1,607,987 4,823,962 2,411,981 7,235,944 3,617,972 1,808,986 904,493 2,713,480 1,356,740 678,370 339,185 1,017,556 508,778 254,389 763,168 381,584 190,792 95,396 47,698 23,849 71,548 35,774 17,887 53,662 26,831 80,494 40,247 120,742 60,371 181,114 90,557 271,672

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