8,467,416

2³ × 3⁴ × 73 × 179

Starting at 8,467,416, the Collatz iteration reaches 1 after 80 steps. The first transition is 4233708; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^4 × 73 × 179

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 24,175,800

Proper Divisor Sum 15,708,384

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #8467409 ← → #8467477

Radix Representation

Decimal	8467416
Binary	100000010011001111011000 (24 bits)
Octal	0o40231730
Hexadecimal	0x8133D8

Divisor Catalog (60 of 80)

1 2 3 4 6 8 9 12 18 24 27 36 54 72 73 81 108 146 162 179 216 219 292 324 358 438 537 584 648 657 716 876 1,074 1,314 1,432 1,611 1,752 1,971 2,148 2,628 3,222 3,942 4,296 4,833 5,256 5,913 6,444 7,884 9,666 11,826 12,888 13,067 14,499 15,768 19,332 23,652 26,134 28,998 38,664 39,201

Collatz Trajectory (80 steps to reach 1)

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

8,467,416 4,233,708 2,116,854 1,058,427 3,175,282 1,587,641 4,762,924 2,381,462 1,190,731 3,572,194 1,786,097 5,358,292 2,679,146 1,339,573 4,018,720 2,009,360 1,004,680 502,340 251,170 125,585 376,756 188,378 94,189 282,568 141,284 70,642 35,321 105,964 52,982 26,491 79,474 39,737 119,212 59,606 29,803 89,410 44,705 134,116 67,058 33,529 100,588 50,294 25,147 75,442 37,721 113,164 56,582 28,291 84,874 42,437 127,312 63,656 31,828 15,914 7,957 23,872 11,936 5,968 2,984 1,492

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