407,772

2² × 3² × 47 × 241

407,772 factors as 2^2 × 3^2 × 47 × 241. Its 36 positive divisors give a proper-divisor sum of 649,284, so this integer is abundant. The Collatz stopping time is 174 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 47 × 241

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 1,057,056

Proper Divisor Sum 649,284

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #407747 ← → #407783

Radix Representation

Decimal	407772
Binary	1100011100011011100 (19 bits)
Octal	0o1434334
Hexadecimal	0x638DC

Divisor Catalog (36)

1 2 3 4 6 9 12 18 36 47 94 141 188 241 282 423 482 564 723 846 964 1,446 1,692 2,169 2,892 4,338 8,676 11,327 22,654 33,981 45,308 67,962 101,943 135,924 203,886 407,772

Collatz Trajectory (174 steps to reach 1)

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

407,772 203,886 101,943 305,830 152,915 458,746 229,373 688,120 344,060 172,030 86,015 258,046 129,023 387,070 193,535 580,606 290,303 870,910 435,455 1,306,366 653,183 1,959,550 979,775 2,939,326 1,469,663 4,408,990 2,204,495 6,613,486 3,306,743 9,920,230 4,960,115 14,880,346 7,440,173 22,320,520 11,160,260 5,580,130 2,790,065 8,370,196 4,185,098 2,092,549 6,277,648 3,138,824 1,569,412 784,706 392,353 1,177,060 588,530 294,265 882,796 441,398 220,699 662,098 331,049 993,148 496,574 248,287 744,862 372,431 1,117,294 558,647

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