221,900

2² × 5² × 7 × 317

Starting at 221,900, the Collatz iteration reaches 1 after 155 steps. The first transition is 110950; the starting value is even with 36 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 7 × 317

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 552,048

Proper Divisor Sum 330,148

Digit Sum / Digital Root 14 (Root: 5)

Adjacent Primes #221891 ← → #221909

Radix Representation

Decimal	221900
Binary	110110001011001100 (18 bits)
Octal	0o661314
Hexadecimal	0x362CC

Divisor Catalog (36)

1 2 4 5 7 10 14 20 25 28 35 50 70 100 140 175 317 350 634 700 1,268 1,585 2,219 3,170 4,438 6,340 7,925 8,876 11,095 15,850 22,190 31,700 44,380 55,475 110,950 221,900

Collatz Trajectory (155 steps to reach 1)

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

221,900 110,950 55,475 166,426 83,213 249,640 124,820 62,410 31,205 93,616 46,808 23,404 11,702 5,851 17,554 8,777 26,332 13,166 6,583 19,750 9,875 29,626 14,813 44,440 22,220 11,110 5,555 16,666 8,333 25,000 12,500 6,250 3,125 9,376 4,688 2,344 1,172 586 293 880 440 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107 322 161 484 242

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