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Atlas › Integer Profiles › Node 27,442,304

27,442,304

27 × 269 × 797
Abundant Even Composite

27,442,304 factors as 2^7 × 269 × 797. Its 32 positive divisors give a proper-divisor sum of 27,499,996, so this integer is abundant. The Collatz stopping time is 79 steps.

Prime Factor Structure

Factorization String 2^7 × 269 × 797
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 54,942,300
Proper Divisor Sum 27,499,996
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #27442277 ← → #27442339

Radix Representation

Decimal 27442304
Binary 1101000101011110010000000 (25 bits)
Octal 0o150536200
Hexadecimal 0x1A2BC80

Divisor Catalog (32)

1 2 4 8 16 32 64 128 269 538 797 1,076 1,594 2,152 3,188 4,304 6,376 8,608 12,752 17,216 25,504 34,432 51,008 102,016 214,393 428,786 857,572 1,715,144 3,430,288 6,860,576 13,721,152 27,442,304

Collatz Trajectory (79 steps to reach 1)

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

27,442,304 13,721,152 6,860,576 3,430,288 1,715,144 857,572 428,786 214,393 643,180 321,590 160,795 482,386 241,193 723,580 361,790 180,895 542,686 271,343 814,030 407,015 1,221,046 610,523 1,831,570 915,785 2,747,356 1,373,678 686,839 2,060,518 1,030,259 3,090,778 1,545,389 4,636,168 2,318,084 1,159,042 579,521 1,738,564 869,282 434,641 1,303,924 651,962 325,981 977,944 488,972 244,486 122,243 366,730 183,365 550,096 275,048 137,524 68,762 34,381 103,144 51,572 25,786 12,893 38,680 19,340 9,670 4,835

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