213,084

2² × 3³ × 1973

213,084 factors as 2^2 × 3^3 × 1973. Its 24 positive divisors give a proper-divisor sum of 339,636, so this integer is abundant. The Collatz stopping time is 173 steps.

Prime Factor Structure

Factorization String 2^2 × 3^3 × 1973

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 552,720

Proper Divisor Sum 339,636

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #213079 ← → #213091

Radix Representation

Decimal	213084
Binary	110100000001011100 (18 bits)
Octal	0o640134
Hexadecimal	0x3405C

Divisor Catalog (24)

1 2 3 4 6 9 12 18 27 36 54 108 1,973 3,946 5,919 7,892 11,838 17,757 23,676 35,514 53,271 71,028 106,542 213,084

Collatz Trajectory (173 steps to reach 1)

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

213,084 106,542 53,271 159,814 79,907 239,722 119,861 359,584 179,792 89,896 44,948 22,474 11,237 33,712 16,856 8,428 4,214 2,107 6,322 3,161 9,484 4,742 2,371 7,114 3,557 10,672 5,336 2,668 1,334 667 2,002 1,001 3,004 1,502 751 2,254 1,127 3,382 1,691 5,074 2,537 7,612 3,806 1,903 5,710 2,855 8,566 4,283 12,850 6,425 19,276 9,638 4,819 14,458 7,229 21,688 10,844 5,422 2,711 8,134

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