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Atlas › Integer Profiles › Node 27,445,210

27,445,210

2 × 5 × 13 × 23 × 67 × 137
Abundant Even Composite

27,445,210 factors as 2 × 5 × 13 × 23 × 67 × 137. Its 64 positive divisors give a proper-divisor sum of 29,309,222, so this integer is abundant. The Collatz stopping time is 237 steps.

Prime Factor Structure

Factorization String 2 × 5 × 13 × 23 × 67 × 137
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 56,754,432
Proper Divisor Sum 29,309,222
Digit Sum / Digital Root 25 (Root: 7)
Adjacent Primes #27445193 ← → #27445213

Radix Representation

Decimal 27445210
Binary 1101000101100011111011010 (25 bits)
Octal 0o150543732
Hexadecimal 0x1A2C7DA

Divisor Catalog (60 of 64)

1 2 5 10 13 23 26 46 65 67 115 130 134 137 230 274 299 335 598 670 685 871 1,370 1,495 1,541 1,742 1,781 2,990 3,082 3,151 3,562 4,355 6,302 7,705 8,710 8,905 9,179 15,410 15,755 17,810 18,358 20,033 31,510 40,066 40,963 45,895 81,926 91,790 100,165 119,327 200,330 204,815 211,117 238,654 409,630 422,234 596,635 1,055,585 1,193,270 2,111,170

Collatz Trajectory (237 steps to reach 1)

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

27,445,210 13,722,605 41,167,816 20,583,908 10,291,954 5,145,977 15,437,932 7,718,966 3,859,483 11,578,450 5,789,225 17,367,676 8,683,838 4,341,919 13,025,758 6,512,879 19,538,638 9,769,319 29,307,958 14,653,979 43,961,938 21,980,969 65,942,908 32,971,454 16,485,727 49,457,182 24,728,591 74,185,774 37,092,887 111,278,662 55,639,331 166,917,994 83,458,997 250,376,992 125,188,496 62,594,248 31,297,124 15,648,562 7,824,281 23,472,844 11,736,422 5,868,211 17,604,634 8,802,317 26,406,952 13,203,476 6,601,738 3,300,869 9,902,608 4,951,304 2,475,652 1,237,826 618,913 1,856,740 928,370 464,185 1,392,556 696,278 348,139 1,044,418

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