780,800

2⁹ × 5² × 61

780,800 factors as 2^9 × 5^2 × 61. Its 60 positive divisors give a proper-divisor sum of 1,185,406, so this integer is abundant. The Collatz stopping time is 118 steps.

Prime Factor Structure

Factorization String 2^9 × 5^2 × 61

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 1,966,206

Proper Divisor Sum 1,185,406

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #780799 ← → #780803

Radix Representation

Decimal	780800
Binary	10111110101000000000 (20 bits)
Octal	0o2765000
Hexadecimal	0xBEA00

Divisor Catalog (60)

1 2 4 5 8 10 16 20 25 32 40 50 61 64 80 100 122 128 160 200 244 256 305 320 400 488 512 610 640 800 976 1,220 1,280 1,525 1,600 1,952 2,440 2,560 3,050 3,200 3,904 4,880 6,100 6,400 7,808 9,760 12,200 12,800 15,616 19,520 24,400 31,232 39,040 48,800 78,080 97,600 156,160 195,200 390,400 780,800

Collatz Trajectory (118 steps to reach 1)

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

780,800 390,400 195,200 97,600 48,800 24,400 12,200 6,100 3,050 1,525 4,576 2,288 1,144 572 286 143 430 215 646 323 970 485 1,456 728 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1,186 593 1,780 890 445 1,336 668 334 167 502 251 754 377 1,132 566 283 850

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