78,800

2⁴ × 5² × 197

For 78,800, the 30 positive divisors have a total of 190,278. Removing 78,800 leaves 111,478, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^4 × 5^2 × 197

Distinct Prime Factors 3

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 30

Divisor Sum (σ) 190,278

Proper Divisor Sum 111,478

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #78797 ← → #78803

Radix Representation

Decimal	78800
Binary	10011001111010000 (17 bits)
Octal	0o231720
Hexadecimal	0x133D0

Divisor Catalog (30)

1 2 4 5 8 10 16 20 25 40 50 80 100 197 200 394 400 788 985 1,576 1,970 3,152 3,940 4,925 7,880 9,850 15,760 19,700 39,400 78,800

Collatz Trajectory (76 steps to reach 1)

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

78,800 39,400 19,700 9,850 4,925 14,776 7,388 3,694 1,847 5,542 2,771 8,314 4,157 12,472 6,236 3,118 1,559 4,678 2,339 7,018 3,509 10,528 5,264 2,632 1,316 658 329 988 494 247 742 371 1,114 557 1,672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88

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