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Atlas › Integer Profiles › Node 27,788,992

27,788,992

26 × 7 × 11 × 5639
Abundant Even Composite

27,788,992 factors as 2^6 × 7 × 11 × 5639. Its 56 positive divisors give a proper-divisor sum of 40,973,888, so this integer is abundant. The Collatz stopping time is 131 steps.

Prime Factor Structure

Factorization String 2^6 × 7 × 11 × 5639
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 56
Divisor Sum (σ) 68,762,880
Proper Divisor Sum 40,973,888
Digit Sum / Digital Root 52 (Root: 7)
Adjacent Primes #27788953 ← → #27789011

Radix Representation

Decimal 27788992
Binary 1101010000000011011000000 (25 bits)
Octal 0o152003300
Hexadecimal 0x1A806C0

Divisor Catalog (56)

1 2 4 7 8 11 14 16 22 28 32 44 56 64 77 88 112 154 176 224 308 352 448 616 704 1,232 2,464 4,928 5,639 11,278 22,556 39,473 45,112 62,029 78,946 90,224 124,058 157,892 180,448 248,116 315,784 360,896 434,203 496,232 631,568 868,406 992,464 1,263,136 1,736,812 1,984,928 2,526,272 3,473,624 3,969,856 6,947,248 13,894,496 27,788,992

Collatz Trajectory (131 steps to reach 1)

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

27,788,992 13,894,496 6,947,248 3,473,624 1,736,812 868,406 434,203 1,302,610 651,305 1,953,916 976,958 488,479 1,465,438 732,719 2,198,158 1,099,079 3,297,238 1,648,619 4,945,858 2,472,929 7,418,788 3,709,394 1,854,697 5,564,092 2,782,046 1,391,023 4,173,070 2,086,535 6,259,606 3,129,803 9,389,410 4,694,705 14,084,116 7,042,058 3,521,029 10,563,088 5,281,544 2,640,772 1,320,386 660,193 1,980,580 990,290 495,145 1,485,436 742,718 371,359 1,114,078 557,039 1,671,118 835,559 2,506,678 1,253,339 3,760,018 1,880,009 5,640,028 2,820,014 1,410,007 4,230,022 2,115,011 6,345,034

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