53,250

2 × 3 × 5³ × 71

Starting at 53,250, the Collatz iteration reaches 1 after 215 steps. The first transition is 26625; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 5^3 × 71

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 134,784

Proper Divisor Sum 81,534

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #53239 ← → #53267

Radix Representation

Decimal	53250
Binary	1101000000000010 (16 bits)
Octal	0o150002
Hexadecimal	0xD002

Divisor Catalog (32)

1 2 3 5 6 10 15 25 30 50 71 75 125 142 150 213 250 355 375 426 710 750 1,065 1,775 2,130 3,550 5,325 8,875 10,650 17,750 26,625 53,250

Collatz Trajectory (215 steps to reach 1)

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

53,250 26,625 79,876 39,938 19,969 59,908 29,954 14,977 44,932 22,466 11,233 33,700 16,850 8,425 25,276 12,638 6,319 18,958 9,479 28,438 14,219 42,658 21,329 63,988 31,994 15,997 47,992 23,996 11,998 5,999 17,998 8,999 26,998 13,499 40,498 20,249 60,748 30,374 15,187 45,562 22,781 68,344 34,172 17,086 8,543 25,630 12,815 38,446 19,223 57,670 28,835 86,506 43,253 129,760 64,880 32,440 16,220 8,110 4,055 12,166

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