472,905

3³ × 5 × 31 × 113

For 472,905, the 32 positive divisors have a total of 875,520. Removing 472,905 leaves 402,615, which gives the deficient classification.

Prime Factor Structure

Factorization String 3^3 × 5 × 31 × 113

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 875,520

Proper Divisor Sum 402,615

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #472883 ← → #472907

Radix Representation

Decimal	472905
Binary	1110011011101001001 (19 bits)
Octal	0o1633511
Hexadecimal	0x73749

Divisor Catalog (32)

1 3 5 9 15 27 31 45 93 113 135 155 279 339 465 565 837 1,017 1,395 1,695 3,051 3,503 4,185 5,085 10,509 15,255 17,515 31,527 52,545 94,581 157,635 472,905

Collatz Trajectory (125 steps to reach 1)

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

472,905 1,418,716 709,358 354,679 1,064,038 532,019 1,596,058 798,029 2,394,088 1,197,044 598,522 299,261 897,784 448,892 224,446 112,223 336,670 168,335 505,006 252,503 757,510 378,755 1,136,266 568,133 1,704,400 852,200 426,100 213,050 106,525 319,576 159,788 79,894 39,947 119,842 59,921 179,764 89,882 44,941 134,824 67,412 33,706 16,853 50,560 25,280 12,640 6,320 3,160 1,580 790 395 1,186 593 1,780 890 445 1,336 668 334 167 502

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