7,873,140

2² × 3 × 5 × 11 × 79 × 151

Starting at 7,873,140, the Collatz iteration reaches 1 after 186 steps. The first transition is 3936570; the starting value is even with 96 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 11 × 79 × 151

Distinct Prime Factors 6

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 24,514,560

Proper Divisor Sum 16,641,420

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #7873133 ← → #7873147

Radix Representation

Decimal	7873140
Binary	11110000010001001110100 (23 bits)
Octal	0o36021164
Hexadecimal	0x782274

Divisor Catalog (60 of 96)

1 2 3 4 5 6 10 11 12 15 20 22 30 33 44 55 60 66 79 110 132 151 158 165 220 237 302 316 330 395 453 474 604 660 755 790 869 906 948 1,185 1,510 1,580 1,661 1,738 1,812 2,265 2,370 2,607 3,020 3,322 3,476 4,345 4,530 4,740 4,983 5,214 6,644 8,305 8,690 9,060

Collatz Trajectory (186 steps to reach 1)

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

7,873,140 3,936,570 1,968,285 5,904,856 2,952,428 1,476,214 738,107 2,214,322 1,107,161 3,321,484 1,660,742 830,371 2,491,114 1,245,557 3,736,672 1,868,336 934,168 467,084 233,542 116,771 350,314 175,157 525,472 262,736 131,368 65,684 32,842 16,421 49,264 24,632 12,316 6,158 3,079 9,238 4,619 13,858 6,929 20,788 10,394 5,197 15,592 7,796 3,898 1,949 5,848 2,924 1,462 731 2,194 1,097 3,292 1,646 823 2,470 1,235 3,706 1,853 5,560 2,780 1,390

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