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Atlas › Integer Profiles › Node 36,968,750

36,968,750

2 × 56 × 7 × 132
Abundant Even Composite

36,968,750 factors as 2 × 5^6 × 7 × 13^2. Its 84 positive divisors give a proper-divisor sum of 48,811,402, so this integer is abundant. The Collatz stopping time is 77 steps.

Prime Factor Structure

Factorization String 2 × 5^6 × 7 × 13^2
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 84
Divisor Sum (σ) 85,780,152
Proper Divisor Sum 48,811,402
Digit Sum / Digital Root 44 (Root: 8)
Adjacent Primes #36968749 ← → #36968753

Radix Representation

Decimal 36968750
Binary 10001101000001100100101110 (26 bits)
Octal 0o215014456
Hexadecimal 0x234192E

Divisor Catalog (60 of 84)

1 2 5 7 10 13 14 25 26 35 50 65 70 91 125 130 169 175 182 250 325 338 350 455 625 650 845 875 910 1,183 1,250 1,625 1,690 1,750 2,275 2,366 3,125 3,250 4,225 4,375 4,550 5,915 6,250 8,125 8,450 8,750 11,375 11,830 15,625 16,250 21,125 21,875 22,750 29,575 31,250 40,625 42,250 43,750 56,875 59,150

Collatz Trajectory (77 steps to reach 1)

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

36,968,750 18,484,375 55,453,126 27,726,563 83,179,690 41,589,845 124,769,536 62,384,768 31,192,384 15,596,192 7,798,096 3,899,048 1,949,524 974,762 487,381 1,462,144 731,072 365,536 182,768 91,384 45,692 22,846 11,423 34,270 17,135 51,406 25,703 77,110 38,555 115,666 57,833 173,500 86,750 43,375 130,126 65,063 195,190 97,595 292,786 146,393 439,180 219,590 109,795 329,386 164,693 494,080 247,040 123,520 61,760 30,880 15,440 7,720 3,860 1,930 965 2,896 1,448 724 362 181

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