88,550

2 × 5² × 7 × 11 × 23

88,550 factors as 2 × 5^2 × 7 × 11 × 23. Its 48 positive divisors give a proper-divisor sum of 125,722, so this integer is abundant. The Collatz stopping time is 164 steps.

Prime Factor Structure

Factorization String 2 × 5^2 × 7 × 11 × 23

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 214,272

Proper Divisor Sum 125,722

Digit Sum / Digital Root 26 (Root: 8)

Adjacent Primes #88547 ← → #88589

Radix Representation

Decimal	88550
Binary	10101100111100110 (17 bits)
Octal	0o254746
Hexadecimal	0x159E6

Divisor Catalog (48)

1 2 5 7 10 11 14 22 23 25 35 46 50 55 70 77 110 115 154 161 175 230 253 275 322 350 385 506 550 575 770 805 1,150 1,265 1,610 1,771 1,925 2,530 3,542 3,850 4,025 6,325 8,050 8,855 12,650 17,710 44,275 88,550

Collatz Trajectory (164 steps to reach 1)

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

88,550 44,275 132,826 66,413 199,240 99,620 49,810 24,905 74,716 37,358 18,679 56,038 28,019 84,058 42,029 126,088 63,044 31,522 15,761 47,284 23,642 11,821 35,464 17,732 8,866 4,433 13,300 6,650 3,325 9,976 4,988 2,494 1,247 3,742 1,871 5,614 2,807 8,422 4,211 12,634 6,317 18,952 9,476 4,738 2,369 7,108 3,554 1,777 5,332 2,666 1,333 4,000 2,000 1,000 500 250 125 376 188 94

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