λ
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Atlas › Integer Profiles › Node 36,917,790

36,917,790

2 × 3 × 5 × 7 × 13 × 13523
Abundant Even Composite

36,917,790 factors as 2 × 3 × 5 × 7 × 13 × 13523. Its 64 positive divisors give a proper-divisor sum of 72,139,746, so this integer is abundant. The Collatz stopping time is 214 steps.

Prime Factor Structure

Factorization String 2 × 3 × 5 × 7 × 13 × 13523
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 109,057,536
Proper Divisor Sum 72,139,746
Digit Sum / Digital Root 42 (Root: 6)
Adjacent Primes #36917789 ← → #36917791

Radix Representation

Decimal 36917790
Binary 10001100110101001000011110 (26 bits)
Octal 0o214651036
Hexadecimal 0x233521E

Divisor Catalog (60 of 64)

1 2 3 5 6 7 10 13 14 15 21 26 30 35 39 42 65 70 78 91 105 130 182 195 210 273 390 455 546 910 1,365 2,730 13,523 27,046 40,569 67,615 81,138 94,661 135,230 175,799 189,322 202,845 283,983 351,598 405,690 473,305 527,397 567,966 878,995 946,610 1,054,794 1,230,593 1,419,915 1,757,990 2,461,186 2,636,985 2,839,830 3,691,779 5,273,970 6,152,965

Collatz Trajectory (214 steps to reach 1)

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

36,917,790 18,458,895 55,376,686 27,688,343 83,065,030 41,532,515 124,597,546 62,298,773 186,896,320 93,448,160 46,724,080 23,362,040 11,681,020 5,840,510 2,920,255 8,760,766 4,380,383 13,141,150 6,570,575 19,711,726 9,855,863 29,567,590 14,783,795 44,351,386 22,175,693 66,527,080 33,263,540 16,631,770 8,315,885 24,947,656 12,473,828 6,236,914 3,118,457 9,355,372 4,677,686 2,338,843 7,016,530 3,508,265 10,524,796 5,262,398 2,631,199 7,893,598 3,946,799 11,840,398 5,920,199 17,760,598 8,880,299 26,640,898 13,320,449 39,961,348 19,980,674 9,990,337 29,971,012 14,985,506 7,492,753 22,478,260 11,239,130 5,619,565 16,858,696 8,429,348

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