λ
Harmonic Matrix

78,744

23 × 3 × 17 × 193
Abundant Even Composite

78,744 has digital root 3. The neighboring primes are 78737 and 78779; its proper-divisor sum differs from the starting integer by 52,032.

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Prime Factor Structure

Factorization String 2^3 × 3 × 17 × 193
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 209,520
Proper Divisor Sum 130,776
Digit Sum / Digital Root 30 (Root: 3)
Adjacent Primes #78737 ← → #78779

Radix Representation

Decimal 78744
Binary 10011001110011000 (17 bits)
Octal 0o231630
Hexadecimal 0x13398

Divisor Catalog (5 of 32)

1 2 3 4 6

Collatz Trajectory (76 steps to reach 1)

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

Showing the first 5 trajectory entries; the stopping-time total above is unchanged.

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