300,768

2⁵ × 3 × 13 × 241

300,768 factors as 2^5 × 3 × 13 × 241. Its 48 positive divisors give a proper-divisor sum of 553,008, so this integer is abundant. The Collatz stopping time is 88 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 13 × 241

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 853,776

Proper Divisor Sum 553,008

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #300761 ← → #300779

Radix Representation

Decimal	300768
Binary	1001001011011100000 (19 bits)
Octal	0o1113340
Hexadecimal	0x496E0

Divisor Catalog (48)

1 2 3 4 6 8 12 13 16 24 26 32 39 48 52 78 96 104 156 208 241 312 416 482 624 723 964 1,248 1,446 1,928 2,892 3,133 3,856 5,784 6,266 7,712 9,399 11,568 12,532 18,798 23,136 25,064 37,596 50,128 75,192 100,256 150,384 300,768

Collatz Trajectory (88 steps to reach 1)

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

300,768 150,384 75,192 37,596 18,798 9,399 28,198 14,099 42,298 21,149 63,448 31,724 15,862 7,931 23,794 11,897 35,692 17,846 8,923 26,770 13,385 40,156 20,078 10,039 30,118 15,059 45,178 22,589 67,768 33,884 16,942 8,471 25,414 12,707 38,122 19,061 57,184 28,592 14,296 7,148 3,574 1,787 5,362 2,681 8,044 4,022 2,011 6,034 3,017 9,052 4,526 2,263 6,790 3,395 10,186 5,093 15,280 7,640 3,820 1,910

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