53,280

2⁵ × 3² × 5 × 37

53,280 factors as 2^5 × 3^2 × 5 × 37. Its 72 positive divisors give a proper-divisor sum of 133,452, so this integer is abundant. The Collatz stopping time is 184 steps.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 37

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 186,732

Proper Divisor Sum 133,452

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #53279 ← → #53281

Radix Representation

Decimal	53280
Binary	1101000000100000 (16 bits)
Octal	0o150040
Hexadecimal	0xD020

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 37 40 45 48 60 72 74 80 90 96 111 120 144 148 160 180 185 222 240 288 296 333 360 370 444 480 555 592 666 720 740 888 1,110 1,184 1,332 1,440 1,480 1,665 1,776 2,220 2,664 2,960

Collatz Trajectory (184 steps to reach 1)

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

53,280 26,640 13,320 6,660 3,330 1,665 4,996 2,498 1,249 3,748 1,874 937 2,812 1,406 703 2,110 1,055 3,166 1,583 4,750 2,375 7,126 3,563 10,690 5,345 16,036 8,018 4,009 12,028 6,014 3,007 9,022 4,511 13,534 6,767 20,302 10,151 30,454 15,227 45,682 22,841 68,524 34,262 17,131 51,394 25,697 77,092 38,546 19,273 57,820 28,910 14,455 43,366 21,683 65,050 32,525 97,576 48,788 24,394 12,197

More profiles

Browse other published profiles and their separate link collections.

No other profiles in this collection.

← Previous Integer #53,279 Browse Full Index Next Integer #53,281 →