684,450

2 × 3⁴ × 5² × 13²

684,450 has the prime decomposition 2 × 3^4 × 5^2 × 13^2. Its 4 distinct prime factors produce 90 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^4 × 5^2 × 13^2

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 90

Divisor Sum (σ) 2,059,299

Proper Divisor Sum 1,374,849

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #684443 ← → #684451

Radix Representation

Decimal	684450
Binary	10100111000110100010 (20 bits)
Octal	0o2470642
Hexadecimal	0xA71A2

Divisor Catalog (60 of 90)

1 2 3 5 6 9 10 13 15 18 25 26 27 30 39 45 50 54 65 75 78 81 90 117 130 135 150 162 169 195 225 234 270 325 338 351 390 405 450 507 585 650 675 702 810 845 975 1,014 1,053 1,170 1,350 1,521 1,690 1,755 1,950 2,025 2,106 2,535 2,925 3,042

Collatz Trajectory (167 steps to reach 1)

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

684,450 342,225 1,026,676 513,338 256,669 770,008 385,004 192,502 96,251 288,754 144,377 433,132 216,566 108,283 324,850 162,425 487,276 243,638 121,819 365,458 182,729 548,188 274,094 137,047 411,142 205,571 616,714 308,357 925,072 462,536 231,268 115,634 57,817 173,452 86,726 43,363 130,090 65,045 195,136 97,568 48,784 24,392 12,196 6,098 3,049 9,148 4,574 2,287 6,862 3,431 10,294 5,147 15,442 7,721 23,164 11,582 5,791 17,374 8,687 26,062

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