7,513,080

2³ × 3 × 5 × 137 × 457

Starting at 7,513,080, the Collatz iteration reaches 1 after 186 steps. The first transition is 3756540; the starting value is even with 64 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 5 × 137 × 457

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 64

Divisor Sum (σ) 22,753,440

Proper Divisor Sum 15,240,360

Digit Sum / Digital Root 24 (Root: 6)

Adjacent Primes #7513073 ← → #7513123

Radix Representation

Decimal	7513080
Binary	11100101010001111111000 (23 bits)
Octal	0o34521770
Hexadecimal	0x72A3F8

Divisor Catalog (60 of 64)

1 2 3 4 5 6 8 10 12 15 20 24 30 40 60 120 137 274 411 457 548 685 822 914 1,096 1,370 1,371 1,644 1,828 2,055 2,285 2,740 2,742 3,288 3,656 4,110 4,570 5,480 5,484 6,855 8,220 9,140 10,968 13,710 16,440 18,280 27,420 54,840 62,609 125,218 187,827 250,436 313,045 375,654 500,872 626,090 751,308 939,135 1,252,180 1,502,616

Collatz Trajectory (186 steps to reach 1)

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

7,513,080 3,756,540 1,878,270 939,135 2,817,406 1,408,703 4,226,110 2,113,055 6,339,166 3,169,583 9,508,750 4,754,375 14,263,126 7,131,563 21,394,690 10,697,345 32,092,036 16,046,018 8,023,009 24,069,028 12,034,514 6,017,257 18,051,772 9,025,886 4,512,943 13,538,830 6,769,415 20,308,246 10,154,123 30,462,370 15,231,185 45,693,556 22,846,778 11,423,389 34,270,168 17,135,084 8,567,542 4,283,771 12,851,314 6,425,657 19,276,972 9,638,486 4,819,243 14,457,730 7,228,865 21,686,596 10,843,298 5,421,649 16,264,948 8,132,474 4,066,237 12,198,712 6,099,356 3,049,678 1,524,839 4,574,518 2,287,259 6,861,778 3,430,889 10,292,668

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