3,684,000

2⁵ × 3 × 5³ × 307

For 3,684,000, the 96 positive divisors have a total of 12,108,096. Removing 3,684,000 leaves 8,424,096, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^5 × 3 × 5^3 × 307

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 12,108,096

Proper Divisor Sum 8,424,096

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #3683993 ← → #3684011

Radix Representation

Decimal	3684000
Binary	1110000011011010100000 (22 bits)
Octal	0o16033240
Hexadecimal	0x3836A0

Divisor Catalog (60 of 96)

1 2 3 4 5 6 8 10 12 15 16 20 24 25 30 32 40 48 50 60 75 80 96 100 120 125 150 160 200 240 250 300 307 375 400 480 500 600 614 750 800 921 1,000 1,200 1,228 1,500 1,535 1,842 2,000 2,400 2,456 3,000 3,070 3,684 4,000 4,605 4,912 6,000 6,140 7,368

Collatz Trajectory (128 steps to reach 1)

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

3,684,000 1,842,000 921,000 460,500 230,250 115,125 345,376 172,688 86,344 43,172 21,586 10,793 32,380 16,190 8,095 24,286 12,143 36,430 18,215 54,646 27,323 81,970 40,985 122,956 61,478 30,739 92,218 46,109 138,328 69,164 34,582 17,291 51,874 25,937 77,812 38,906 19,453 58,360 29,180 14,590 7,295 21,886 10,943 32,830 16,415 49,246 24,623 73,870 36,935 110,806 55,403 166,210 83,105 249,316 124,658 62,329 186,988 93,494 46,747 140,242

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