57,726,960

2⁴ × 3 × 5 × 31 × 7759

57,726,960 factors as 2^4 × 3 × 5 × 31 × 7759. Its 80 positive divisors give a proper-divisor sum of 127,023,120, so this integer is abundant. The Collatz stopping time is 119 steps.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 31 × 7759

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 184,750,080

Proper Divisor Sum 127,023,120

Digit Sum / Digital Root 42 (Root: 6)

Adjacent Primes #57726953 ← → #57726967

Radix Representation

Decimal	57726960
Binary	11011100001101011111110000 (26 bits)
Octal	0o334153760
Hexadecimal	0x370D7F0

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 31 40 48 60 62 80 93 120 124 155 186 240 248 310 372 465 496 620 744 930 1,240 1,488 1,860 2,480 3,720 7,440 7,759 15,518 23,277 31,036 38,795 46,554 62,072 77,590 93,108 116,385 124,144 155,180 186,216 232,770 240,529 310,360 372,432 465,540 481,058 620,720

Collatz Trajectory (119 steps to reach 1)

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

57,726,960 28,863,480 14,431,740 7,215,870 3,607,935 10,823,806 5,411,903 16,235,710 8,117,855 24,353,566 12,176,783 36,530,350 18,265,175 54,795,526 27,397,763 82,193,290 41,096,645 123,289,936 61,644,968 30,822,484 15,411,242 7,705,621 23,116,864 11,558,432 5,779,216 2,889,608 1,444,804 722,402 361,201 1,083,604 541,802 270,901 812,704 406,352 203,176 101,588 50,794 25,397 76,192 38,096 19,048 9,524 4,762 2,381 7,144 3,572 1,786 893 2,680 1,340 670 335 1,006 503 1,510 755 2,266 1,133 3,400 1,700

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