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Atlas › Integer Profiles › Node 27,116,560

27,116,560

24 × 5 × 37 × 9161
Abundant Even Composite

27,116,560 factors as 2^4 × 5 × 37 × 9161. Its 40 positive divisors give a proper-divisor sum of 37,640,456, so this integer is abundant. The Collatz stopping time is 131 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 37 × 9161
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 64,757,016
Proper Divisor Sum 37,640,456
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #27116527 ← → #27116561

Radix Representation

Decimal 27116560
Binary 1100111011100010000010000 (25 bits)
Octal 0o147342020
Hexadecimal 0x19DC410

Divisor Catalog (40)

1 2 4 5 8 10 16 20 37 40 74 80 148 185 296 370 592 740 1,480 2,960 9,161 18,322 36,644 45,805 73,288 91,610 146,576 183,220 338,957 366,440 677,914 732,880 1,355,828 1,694,785 2,711,656 3,389,570 5,423,312 6,779,140 13,558,280 27,116,560

Collatz Trajectory (131 steps to reach 1)

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

27,116,560 13,558,280 6,779,140 3,389,570 1,694,785 5,084,356 2,542,178 1,271,089 3,813,268 1,906,634 953,317 2,859,952 1,429,976 714,988 357,494 178,747 536,242 268,121 804,364 402,182 201,091 603,274 301,637 904,912 452,456 226,228 113,114 56,557 169,672 84,836 42,418 21,209 63,628 31,814 15,907 47,722 23,861 71,584 35,792 17,896 8,948 4,474 2,237 6,712 3,356 1,678 839 2,518 1,259 3,778 1,889 5,668 2,834 1,417 4,252 2,126 1,063 3,190 1,595 4,786

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