516,600

2³ × 3² × 5² × 7 × 41

516,600 factors as 2^3 × 3^2 × 5^2 × 7 × 41. Its 144 positive divisors give a proper-divisor sum of 1,514,520, so this integer is abundant. The Collatz stopping time is 89 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 5^2 × 7 × 41

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 2,031,120

Proper Divisor Sum 1,514,520

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #516599 ← → #516611

Radix Representation

Decimal	516600
Binary	1111110000111111000 (19 bits)
Octal	0o1760770
Hexadecimal	0x7E1F8

Divisor Catalog (60 of 144)

1 2 3 4 5 6 7 8 9 10 12 14 15 18 20 21 24 25 28 30 35 36 40 41 42 45 50 56 60 63 70 72 75 82 84 90 100 105 120 123 126 140 150 164 168 175 180 200 205 210 225 246 252 280 287 300 315 328 350 360

Collatz Trajectory (89 steps to reach 1)

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

516,600 258,300 129,150 64,575 193,726 96,863 290,590 145,295 435,886 217,943 653,830 326,915 980,746 490,373 1,471,120 735,560 367,780 183,890 91,945 275,836 137,918 68,959 206,878 103,439 310,318 155,159 465,478 232,739 698,218 349,109 1,047,328 523,664 261,832 130,916 65,458 32,729 98,188 49,094 24,547 73,642 36,821 110,464 55,232 27,616 13,808 6,904 3,452 1,726 863 2,590 1,295 3,886 1,943 5,830 2,915 8,746 4,373 13,120 6,560 3,280

More profiles

Browse other published profiles and their separate link collections.

No other profiles in this collection.

← Previous Integer #516,599 Browse Full Index Next Integer #516,601 →