8,348,632

2³ × 17² × 23 × 157

Starting at 8,348,632, the Collatz iteration reaches 1 after 199 steps. The first transition is 4174316; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 17^2 × 23 × 157

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 17,462,160

Proper Divisor Sum 9,113,528

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #8348629 ← → #8348633

Radix Representation

Decimal	8348632
Binary	11111110110001111011000 (23 bits)
Octal	0o37661730
Hexadecimal	0x7F63D8

Divisor Catalog (48)

1 2 4 8 17 23 34 46 68 92 136 157 184 289 314 391 578 628 782 1,156 1,256 1,564 2,312 2,669 3,128 3,611 5,338 6,647 7,222 10,676 13,294 14,444 21,352 26,588 28,888 45,373 53,176 61,387 90,746 122,774 181,492 245,548 362,984 491,096 1,043,579 2,087,158 4,174,316 8,348,632

Collatz Trajectory (199 steps to reach 1)

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

8,348,632 4,174,316 2,087,158 1,043,579 3,130,738 1,565,369 4,696,108 2,348,054 1,174,027 3,522,082 1,761,041 5,283,124 2,641,562 1,320,781 3,962,344 1,981,172 990,586 495,293 1,485,880 742,940 371,470 185,735 557,206 278,603 835,810 417,905 1,253,716 626,858 313,429 940,288 470,144 235,072 117,536 58,768 29,384 14,692 7,346 3,673 11,020 5,510 2,755 8,266 4,133 12,400 6,200 3,100 1,550 775 2,326 1,163 3,490 1,745 5,236 2,618 1,309 3,928 1,964 982 491 1,474

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