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Atlas › Integer Profiles › Node 42,579,360

42,579,360

25 × 32 × 5 × 29569
Abundant Even Composite

42,579,360 factors as 2^5 × 3^2 × 5 × 29569. Its 72 positive divisors give a proper-divisor sum of 102,727,620, so this integer is abundant. The Collatz stopping time is 98 steps.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5 × 29569
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 145,306,980
Proper Divisor Sum 102,727,620
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #42579359 ← → #42579391

Radix Representation

Decimal 42579360
Binary 10100010011011010110100000 (26 bits)
Octal 0o242332640
Hexadecimal 0x289B5A0

Divisor Catalog (60 of 72)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 30 32 36 40 45 48 60 72 80 90 96 120 144 160 180 240 288 360 480 720 1,440 29,569 59,138 88,707 118,276 147,845 177,414 236,552 266,121 295,690 354,828 443,535 473,104 532,242 591,380 709,656 887,070 946,208 1,064,484 1,182,760 1,330,605 1,419,312 1,774,140 2,128,968 2,365,520

Collatz Trajectory (98 steps to reach 1)

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

42,579,360 21,289,680 10,644,840 5,322,420 2,661,210 1,330,605 3,991,816 1,995,908 997,954 498,977 1,496,932 748,466 374,233 1,122,700 561,350 280,675 842,026 421,013 1,263,040 631,520 315,760 157,880 78,940 39,470 19,735 59,206 29,603 88,810 44,405 133,216 66,608 33,304 16,652 8,326 4,163 12,490 6,245 18,736 9,368 4,684 2,342 1,171 3,514 1,757 5,272 2,636 1,318 659 1,978 989 2,968 1,484 742 371 1,114 557 1,672 836 418 209

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