123,900

2² × 3 × 5² × 7 × 59

123,900 has the prime decomposition 2^2 × 3 × 5^2 × 7 × 59. Its 5 distinct prime factors produce 72 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^2 × 7 × 59

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 416,640

Proper Divisor Sum 292,740

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #123887 ← → #123911

Radix Representation

Decimal	123900
Binary	11110001111111100 (17 bits)
Octal	0o361774
Hexadecimal	0x1E3FC

Divisor Catalog (60 of 72)

1 2 3 4 5 6 7 10 12 14 15 20 21 25 28 30 35 42 50 59 60 70 75 84 100 105 118 140 150 175 177 210 236 295 300 350 354 413 420 525 590 700 708 826 885 1,050 1,180 1,239 1,475 1,652 1,770 2,065 2,100 2,478 2,950 3,540 4,130 4,425 4,956 5,900

Collatz Trajectory (61 steps to reach 1)

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

123,900 61,950 30,975 92,926 46,463 139,390 69,695 209,086 104,543 313,630 156,815 470,446 235,223 705,670 352,835 1,058,506 529,253 1,587,760 793,880 396,940 198,470 99,235 297,706 148,853 446,560 223,280 111,640 55,820 27,910 13,955 41,866 20,933 62,800 31,400 15,700 7,850 3,925 11,776 5,888 2,944 1,472 736 368 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4

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