7,991,672

2³ × 13² × 23 × 257

7,991,672 has the prime decomposition 2^3 × 13^2 × 23 × 257. Its 4 distinct prime factors produce 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 13^2 × 23 × 257

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 16,997,040

Proper Divisor Sum 9,005,368

Digit Sum / Digital Root 41 (Root: 5)

Adjacent Primes #7991657 ← → #7991701

Radix Representation

Decimal	7991672
Binary	11110011111000101111000 (23 bits)
Octal	0o36370570
Hexadecimal	0x79F178

Divisor Catalog (48)

1 2 4 8 13 23 26 46 52 92 104 169 184 257 299 338 514 598 676 1,028 1,196 1,352 2,056 2,392 3,341 3,887 5,911 6,682 7,774 11,822 13,364 15,548 23,644 26,728 31,096 43,433 47,288 76,843 86,866 153,686 173,732 307,372 347,464 614,744 998,959 1,997,918 3,995,836 7,991,672

Collatz Trajectory (336 steps to reach 1)

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

7,991,672 3,995,836 1,997,918 998,959 2,996,878 1,498,439 4,495,318 2,247,659 6,742,978 3,371,489 10,114,468 5,057,234 2,528,617 7,585,852 3,792,926 1,896,463 5,689,390 2,844,695 8,534,086 4,267,043 12,801,130 6,400,565 19,201,696 9,600,848 4,800,424 2,400,212 1,200,106 600,053 1,800,160 900,080 450,040 225,020 112,510 56,255 168,766 84,383 253,150 126,575 379,726 189,863 569,590 284,795 854,386 427,193 1,281,580 640,790 320,395 961,186 480,593 1,441,780 720,890 360,445 1,081,336 540,668 270,334 135,167 405,502 202,751 608,254 304,127

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