λ
Harmonic Matrix

34,344

23 × 34 × 53
Abundant Even Composite

34,344 has digital root 9. The neighboring primes are 34337 and 34351; its proper-divisor sum differs from the starting integer by 29,322.

Prime Factor Structure

Factorization String 2^3 × 3^4 × 53
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 98,010
Proper Divisor Sum 63,666
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #34337 ← → #34351

Radix Representation

Decimal 34344
Binary 1000011000101000 (16 bits)
Octal 0o103050
Hexadecimal 0x8628

Divisor Catalog (40)

1 2 3 4 6 8 9 12 18 24 27 36 53 54 72 81 106 108 159 162 212 216 318 324 424 477 636 648 954 1,272 1,431 1,908 2,862 3,816 4,293 5,724 8,586 11,448 17,172 34,344

Collatz Trajectory (28 steps to reach 1)

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

34,344 17,172 8,586 4,293 12,880 6,440 3,220 1,610 805 2,416 1,208 604 302 151 454 227 682 341 1,024 512 256 128 64 32 16 8 4 2 1

More profiles

← Previous Integer #34,343 Browse Full Index Next Integer #34,345 →