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7,686,400

28 × 52 × 1201
Abundant Even Composite

7,686,400 factors as 2^8 × 5^2 × 1201. Its 54 positive divisors give a proper-divisor sum of 11,354,482, so this integer is abundant. The Collatz stopping time is 72 steps.

Prime Factor Structure

Factorization String 2^8 × 5^2 × 1201
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 54
Divisor Sum (σ) 19,040,882
Proper Divisor Sum 11,354,482
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #7686391 ← → #7686443

Radix Representation

Decimal 7686400
Binary 11101010100100100000000 (23 bits)
Octal 0o35244400
Hexadecimal 0x754900

Divisor Catalog (54)

1 2 4 5 8 10 16 20 25 32 40 50 64 80 100 128 160 200 256 320 400 640 800 1,201 1,280 1,600 2,402 3,200 4,804 6,005 6,400 9,608 12,010 19,216 24,020 30,025 38,432 48,040 60,050 76,864 96,080 120,100 153,728 192,160 240,200 307,456 384,320 480,400 768,640 960,800 1,537,280 1,921,600 3,843,200 7,686,400

Collatz Trajectory (72 steps to reach 1)

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

7,686,400 3,843,200 1,921,600 960,800 480,400 240,200 120,100 60,050 30,025 90,076 45,038 22,519 67,558 33,779 101,338 50,669 152,008 76,004 38,002 19,001 57,004 28,502 14,251 42,754 21,377 64,132 32,066 16,033 48,100 24,050 12,025 36,076 18,038 9,019 27,058 13,529 40,588 20,294 10,147 30,442 15,221 45,664 22,832 11,416 5,708 2,854 1,427 4,282 2,141 6,424 3,212 1,606 803 2,410 1,205 3,616 1,808 904 452 226

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