52,005,672

2³ × 3³ × 61 × 3947

52,005,672 factors as 2^3 × 3^3 × 61 × 3947. Its 64 positive divisors give a proper-divisor sum of 94,859,928, so this integer is abundant. The Collatz stopping time is 155 steps.

Prime Factor Structure

Factorization String 2^3 × 3^3 × 61 × 3947

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 146,865,600

Proper Divisor Sum 94,859,928

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #52005661 ← → #52005689

Radix Representation

Decimal	52005672
Binary	11000110011000101100101000 (26 bits)
Octal	0o306305450
Hexadecimal	0x3198B28

Divisor Catalog (60 of 64)

1 2 3 4 6 8 9 12 18 24 27 36 54 61 72 108 122 183 216 244 366 488 549 732 1,098 1,464 1,647 2,196 3,294 3,947 4,392 6,588 7,894 11,841 13,176 15,788 23,682 31,576 35,523 47,364 71,046 94,728 106,569 142,092 213,138 240,767 284,184 426,276 481,534 722,301 852,552 963,068 1,444,602 1,926,136 2,166,903 2,889,204 4,333,806 5,778,408 6,500,709 8,667,612

Collatz Trajectory (155 steps to reach 1)

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

52,005,672 26,002,836 13,001,418 6,500,709 19,502,128 9,751,064 4,875,532 2,437,766 1,218,883 3,656,650 1,828,325 5,484,976 2,742,488 1,371,244 685,622 342,811 1,028,434 514,217 1,542,652 771,326 385,663 1,156,990 578,495 1,735,486 867,743 2,603,230 1,301,615 3,904,846 1,952,423 5,857,270 2,928,635 8,785,906 4,392,953 13,178,860 6,589,430 3,294,715 9,884,146 4,942,073 14,826,220 7,413,110 3,706,555 11,119,666 5,559,833 16,679,500 8,339,750 4,169,875 12,509,626 6,254,813 18,764,440 9,382,220 4,691,110 2,345,555 7,036,666 3,518,333 10,555,000 5,277,500 2,638,750 1,319,375 3,958,126 1,979,063

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