8,132,340

2² × 3 × 5 × 23 × 71 × 83

Starting at 8,132,340, the Collatz iteration reaches 1 after 85 steps. The first transition is 4066170; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 23 × 71 × 83

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 24,385,536

Proper Divisor Sum 16,253,196

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #8132329 ← → #8132347

Radix Representation

Decimal	8132340
Binary	11111000001011011110100 (23 bits)
Octal	0o37013364
Hexadecimal	0x7C16F4

Divisor Catalog (60 of 96)

1 2 3 4 5 6 10 12 15 20 23 30 46 60 69 71 83 92 115 138 142 166 213 230 249 276 284 332 345 355 415 426 460 498 690 710 830 852 996 1,065 1,245 1,380 1,420 1,633 1,660 1,909 2,130 2,490 3,266 3,818 4,260 4,899 4,980 5,727 5,893 6,532 7,636 8,165 9,545 9,798

Collatz Trajectory (85 steps to reach 1)

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

8,132,340 4,066,170 2,033,085 6,099,256 3,049,628 1,524,814 762,407 2,287,222 1,143,611 3,430,834 1,715,417 5,146,252 2,573,126 1,286,563 3,859,690 1,929,845 5,789,536 2,894,768 1,447,384 723,692 361,846 180,923 542,770 271,385 814,156 407,078 203,539 610,618 305,309 915,928 457,964 228,982 114,491 343,474 171,737 515,212 257,606 128,803 386,410 193,205 579,616 289,808 144,904 72,452 36,226 18,113 54,340 27,170 13,585 40,756 20,378 10,189 30,568 15,284 7,642 3,821 11,464 5,732 2,866 1,433

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