λ
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Atlas › Integer Profiles › Node 36,970,740

36,970,740

22 × 32 × 5 × 293 × 701
Abundant Even Composite

36,970,740 factors as 2^2 × 3^2 × 5 × 293 × 701. Its 72 positive divisors give a proper-divisor sum of 75,717,108, so this integer is abundant. The Collatz stopping time is 165 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 5 × 293 × 701
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 112,687,848
Proper Divisor Sum 75,717,108
Digit Sum / Digital Root 36 (Root: 9)
Adjacent Primes #36970727 ← → #36970741

Radix Representation

Decimal 36970740
Binary 10001101000010000011110100 (26 bits)
Octal 0o215020364
Hexadecimal 0x23420F4

Divisor Catalog (60 of 72)

1 2 3 4 5 6 9 10 12 15 18 20 30 36 45 60 90 180 293 586 701 879 1,172 1,402 1,465 1,758 2,103 2,637 2,804 2,930 3,505 3,516 4,206 4,395 5,274 5,860 6,309 7,010 8,412 8,790 10,515 10,548 12,618 13,185 14,020 17,580 21,030 25,236 26,370 31,545 42,060 52,740 63,090 126,180 205,393 410,786 616,179 821,572 1,026,965 1,232,358

Collatz Trajectory (165 steps to reach 1)

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

36,970,740 18,485,370 9,242,685 27,728,056 13,864,028 6,932,014 3,466,007 10,398,022 5,199,011 15,597,034 7,798,517 23,395,552 11,697,776 5,848,888 2,924,444 1,462,222 731,111 2,193,334 1,096,667 3,290,002 1,645,001 4,935,004 2,467,502 1,233,751 3,701,254 1,850,627 5,551,882 2,775,941 8,327,824 4,163,912 2,081,956 1,040,978 520,489 1,561,468 780,734 390,367 1,171,102 585,551 1,756,654 878,327 2,634,982 1,317,491 3,952,474 1,976,237 5,928,712 2,964,356 1,482,178 741,089 2,223,268 1,111,634 555,817 1,667,452 833,726 416,863 1,250,590 625,295 1,875,886 937,943 2,813,830 1,406,915

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