λ
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Atlas › Integer Profiles › Node 27,000,700

27,000,700

22 × 52 × 193 × 1399
Abundant Even Composite

27,000,700 factors as 2^2 × 5^2 × 193 × 1399. Its 36 positive divisors give a proper-divisor sum of 31,936,500, so this integer is abundant. The Collatz stopping time is 273 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 193 × 1399
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 58,937,200
Proper Divisor Sum 31,936,500
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #27000679 ← → #27000707

Radix Representation

Decimal 27000700
Binary 1100110111111111101111100 (25 bits)
Octal 0o146777574
Hexadecimal 0x19BFF7C

Divisor Catalog (36)

1 2 4 5 10 20 25 50 100 193 386 772 965 1,399 1,930 2,798 3,860 4,825 5,596 6,995 9,650 13,990 19,300 27,980 34,975 69,950 139,900 270,007 540,014 1,080,028 1,350,035 2,700,070 5,400,140 6,750,175 13,500,350 27,000,700

Collatz Trajectory (273 steps to reach 1)

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

27,000,700 13,500,350 6,750,175 20,250,526 10,125,263 30,375,790 15,187,895 45,563,686 22,781,843 68,345,530 34,172,765 102,518,296 51,259,148 25,629,574 12,814,787 38,444,362 19,222,181 57,666,544 28,833,272 14,416,636 7,208,318 3,604,159 10,812,478 5,406,239 16,218,718 8,109,359 24,328,078 12,164,039 36,492,118 18,246,059 54,738,178 27,369,089 82,107,268 41,053,634 20,526,817 61,580,452 30,790,226 15,395,113 46,185,340 23,092,670 11,546,335 34,639,006 17,319,503 51,958,510 25,979,255 77,937,766 38,968,883 116,906,650 58,453,325 175,359,976 87,679,988 43,839,994 21,919,997 65,759,992 32,879,996 16,439,998 8,219,999 24,659,998 12,329,999 36,989,998

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