29,538,040

2³ × 5 × 7 × 31 × 41 × 83

29,538,040 factors as 2^3 × 5 × 7 × 31 × 41 × 83. Its 128 positive divisors give a proper-divisor sum of 51,747,080, so this integer is abundant. The Collatz stopping time is 175 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 31 × 41 × 83

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 128

Divisor Sum (σ) 81,285,120

Proper Divisor Sum 51,747,080

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #29538017 ← → #29538077

Radix Representation

Decimal	29538040
Binary	1110000101011011011111000 (25 bits)
Octal	0o160533370
Hexadecimal	0x1C2B6F8

Divisor Catalog (60 of 128)

1 2 4 5 7 8 10 14 20 28 31 35 40 41 56 62 70 82 83 124 140 155 164 166 205 217 248 280 287 310 328 332 410 415 434 574 581 620 664 820 830 868 1,085 1,148 1,162 1,240 1,271 1,435 1,640 1,660 1,736 2,170 2,296 2,324 2,542 2,573 2,870 2,905 3,320 3,403

Collatz Trajectory (175 steps to reach 1)

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

29,538,040 14,769,020 7,384,510 3,692,255 11,076,766 5,538,383 16,615,150 8,307,575 24,922,726 12,461,363 37,384,090 18,692,045 56,076,136 28,038,068 14,019,034 7,009,517 21,028,552 10,514,276 5,257,138 2,628,569 7,885,708 3,942,854 1,971,427 5,914,282 2,957,141 8,871,424 4,435,712 2,217,856 1,108,928 554,464 277,232 138,616 69,308 34,654 17,327 51,982 25,991 77,974 38,987 116,962 58,481 175,444 87,722 43,861 131,584 65,792 32,896 16,448 8,224 4,112 2,056 1,028 514 257 772 386 193 580 290 145

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