7,584,402

2 × 3 × 7 × 89 × 2029

Starting at 7,584,402, the Collatz iteration reaches 1 after 217 steps. The first transition is 3792201; the starting value is even with 32 positive divisors.

Prime Factor Structure

Factorization String 2 × 3 × 7 × 89 × 2029

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 17,539,200

Proper Divisor Sum 9,954,798

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7584389 ← → #7584407

Radix Representation

Decimal	7584402
Binary	11100111011101010010010 (23 bits)
Octal	0o34735222
Hexadecimal	0x73BA92

Divisor Catalog (32)

1 2 3 6 7 14 21 42 89 178 267 534 623 1,246 1,869 2,029 3,738 4,058 6,087 12,174 14,203 28,406 42,609 85,218 180,581 361,162 541,743 1,083,486 1,264,067 2,528,134 3,792,201 7,584,402

Collatz Trajectory (217 steps to reach 1)

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

7,584,402 3,792,201 11,376,604 5,688,302 2,844,151 8,532,454 4,266,227 12,798,682 6,399,341 19,198,024 9,599,012 4,799,506 2,399,753 7,199,260 3,599,630 1,799,815 5,399,446 2,699,723 8,099,170 4,049,585 12,148,756 6,074,378 3,037,189 9,111,568 4,555,784 2,277,892 1,138,946 569,473 1,708,420 854,210 427,105 1,281,316 640,658 320,329 960,988 480,494 240,247 720,742 360,371 1,081,114 540,557 1,621,672 810,836 405,418 202,709 608,128 304,064 152,032 76,016 38,008 19,004 9,502 4,751 14,254 7,127 21,382 10,691 32,074 16,037 48,112

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