47,928

2³ × 3 × 1997

47,928 factors as 2^3 × 3 × 1997. Its 16 positive divisors give a proper-divisor sum of 71,952, so this integer is abundant. The Collatz stopping time is 96 steps.

Prime Factor Structure

Factorization String 2^3 × 3 × 1997

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 119,880

Proper Divisor Sum 71,952

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #47917 ← → #47933

Radix Representation

Decimal	47928
Binary	1011101100111000 (16 bits)
Octal	0o135470
Hexadecimal	0xBB38

Divisor Catalog (16)

1 2 3 4 6 8 12 24 1,997 3,994 5,991 7,988 11,982 15,976 23,964 47,928

Collatz Trajectory (96 steps to reach 1)

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

47,928 23,964 11,982 5,991 17,974 8,987 26,962 13,481 40,444 20,222 10,111 30,334 15,167 45,502 22,751 68,254 34,127 102,382 51,191 153,574 76,787 230,362 115,181 345,544 172,772 86,386 43,193 129,580 64,790 32,395 97,186 48,593 145,780 72,890 36,445 109,336 54,668 27,334 13,667 41,002 20,501 61,504 30,752 15,376 7,688 3,844 1,922 961 2,884 1,442 721 2,164 1,082 541 1,624 812 406 203 610 305

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