39,480

2³ × 3 × 5 × 7 × 47

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 7 × 47

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 138,240

Proper Divisor Sum 98,760

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #39461 ← → #39499

Radix Representation

Decimal	39480
Binary	1001101000111000 (16 bits)
Octal	0o115070
Hexadecimal	0x9A38

Divisor Catalog (60 of 64)

1 2 3 4 5 6 7 8 10 12 14 15 20 21 24 28 30 35 40 42 47 56 60 70 84 94 105 120 140 141 168 188 210 235 280 282 329 376 420 470 564 658 705 840 940 987 1,128 1,316 1,410 1,645 1,880 1,974 2,632 2,820 3,290 3,948 4,935 5,640 6,580 7,896

Collatz Trajectory (199 steps to reach 1)

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

39,480 19,740 9,870 4,935 14,806 7,403 22,210 11,105 33,316 16,658 8,329 24,988 12,494 6,247 18,742 9,371 28,114 14,057 42,172 21,086 10,543 31,630 15,815 47,446 23,723 71,170 35,585 106,756 53,378 26,689 80,068 40,034 20,017 60,052 30,026 15,013 45,040 22,520 11,260 5,630 2,815 8,446 4,223 12,670 6,335 19,006 9,503 28,510 14,255 42,766 21,383 64,150 32,075 96,226 48,113 144,340 72,170 36,085 108,256 54,128

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