77,282,016

2⁵ × 3 × 7³ × 2347

77,282,016 factors as 2^5 × 3 × 7^3 × 2347. Its 96 positive divisors give a proper-divisor sum of 159,396,384, so this integer is abundant. The Collatz stopping time is 166 steps.

Prime Factor Structure

Factorization String 2^5 × 3 × 7^3 × 2347

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 96

Divisor Sum (σ) 236,678,400

Proper Divisor Sum 159,396,384

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #77281969 ← → #77282027

Radix Representation

Decimal	77282016
Binary	100100110110011101011100000 (27 bits)
Octal	0o446635340
Hexadecimal	0x49B3AE0

Divisor Catalog (60 of 96)

1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 49 56 84 96 98 112 147 168 196 224 294 336 343 392 588 672 686 784 1,029 1,176 1,372 1,568 2,058 2,347 2,352 2,744 4,116 4,694 4,704 5,488 7,041 8,232 9,388 10,976 14,082 16,429 16,464 18,776 28,164 32,858 32,928 37,552 49,287 56,328

Collatz Trajectory (166 steps to reach 1)

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

77,282,016 38,641,008 19,320,504 9,660,252 4,830,126 2,415,063 7,245,190 3,622,595 10,867,786 5,433,893 16,301,680 8,150,840 4,075,420 2,037,710 1,018,855 3,056,566 1,528,283 4,584,850 2,292,425 6,877,276 3,438,638 1,719,319 5,157,958 2,578,979 7,736,938 3,868,469 11,605,408 5,802,704 2,901,352 1,450,676 725,338 362,669 1,088,008 544,004 272,002 136,001 408,004 204,002 102,001 306,004 153,002 76,501 229,504 114,752 57,376 28,688 14,344 7,172 3,586 1,793 5,380 2,690 1,345 4,036 2,018 1,009 3,028 1,514 757 2,272

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