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77,520

24 × 3 × 5 × 17 × 19
Abundant Even Composite

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 17 × 19
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 80
Divisor Sum (σ) 267,840
Proper Divisor Sum 190,320
Digit Sum / Digital Root 21 (Root: 3)
Adjacent Primes #77513 ← → #77521

Radix Representation

Decimal 77520
Binary 10010111011010000 (17 bits)
Octal 0o227320
Hexadecimal 0x12ED0

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 17 19 20 24 30 34 38 40 48 51 57 60 68 76 80 85 95 102 114 120 136 152 170 190 204 228 240 255 272 285 304 323 340 380 408 456 510 570 646 680 760 816 912 969 1,020 1,140 1,292 1,360 1,520

Collatz Trajectory (76 steps to reach 1)

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

77,520 38,760 19,380 9,690 4,845 14,536 7,268 3,634 1,817 5,452 2,726 1,363 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727 5,182 2,591 7,774 3,887 11,662 5,831 17,494 8,747 26,242 13,121 39,364 19,682 9,841 29,524 14,762 7,381 22,144 11,072 5,536 2,768 1,384 692 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14

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