770,800

2⁴ × 5² × 41 × 47

770,800 factors as 2^4 × 5^2 × 41 × 47. Its 60 positive divisors give a proper-divisor sum of 1,166,576, so this integer is abundant. The Collatz stopping time is 149 steps.

Prime Factor Structure

Factorization String 2^4 × 5^2 × 41 × 47

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 1,937,376

Proper Divisor Sum 1,166,576

Digit Sum / Digital Root 22 (Root: 4)

Adjacent Primes #770789 ← → #770801

Radix Representation

Decimal	770800
Binary	10111100001011110000 (20 bits)
Octal	0o2741360
Hexadecimal	0xBC2F0

Divisor Catalog (60)

1 2 4 5 8 10 16 20 25 40 41 47 50 80 82 94 100 164 188 200 205 235 328 376 400 410 470 656 752 820 940 1,025 1,175 1,640 1,880 1,927 2,050 2,350 3,280 3,760 3,854 4,100 4,700 7,708 8,200 9,400 9,635 15,416 16,400 18,800 19,270 30,832 38,540 48,175 77,080 96,350 154,160 192,700 385,400 770,800

Collatz Trajectory (149 steps to reach 1)

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

770,800 385,400 192,700 96,350 48,175 144,526 72,263 216,790 108,395 325,186 162,593 487,780 243,890 121,945 365,836 182,918 91,459 274,378 137,189 411,568 205,784 102,892 51,446 25,723 77,170 38,585 115,756 57,878 28,939 86,818 43,409 130,228 65,114 32,557 97,672 48,836 24,418 12,209 36,628 18,314 9,157 27,472 13,736 6,868 3,434 1,717 5,152 2,576 1,288 644 322 161 484 242 121 364 182 91 274 137

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