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Atlas › Integer Profiles › Node 27,774,110

27,774,110

2 × 5 × 7 × 13 × 23 × 1327
Abundant Even Composite

27,774,110 factors as 2 × 5 × 7 × 13 × 23 × 1327. Its 64 positive divisors give a proper-divisor sum of 36,479,842, so this integer is abundant. The Collatz stopping time is 211 steps.

Prime Factor Structure

Factorization String 2 × 5 × 7 × 13 × 23 × 1327
Distinct Prime Factors 6
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 64,253,952
Proper Divisor Sum 36,479,842
Digit Sum / Digital Root 29 (Root: 2)
Adjacent Primes #27774079 ← → #27774119

Radix Representation

Decimal 27774110
Binary 1101001111100110010011110 (25 bits)
Octal 0o151746236
Hexadecimal 0x1A7CC9E

Divisor Catalog (60 of 64)

1 2 5 7 10 13 14 23 26 35 46 65 70 91 115 130 161 182 230 299 322 455 598 805 910 1,327 1,495 1,610 2,093 2,654 2,990 4,186 6,635 9,289 10,465 13,270 17,251 18,578 20,930 30,521 34,502 46,445 61,042 86,255 92,890 120,757 152,605 172,510 213,647 241,514 305,210 396,773 427,294 603,785 793,546 1,068,235 1,207,570 1,983,865 2,136,470 2,777,411

Collatz Trajectory (211 steps to reach 1)

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

27,774,110 13,887,055 41,661,166 20,830,583 62,491,750 31,245,875 93,737,626 46,868,813 140,606,440 70,303,220 35,151,610 17,575,805 52,727,416 26,363,708 13,181,854 6,590,927 19,772,782 9,886,391 29,659,174 14,829,587 44,488,762 22,244,381 66,733,144 33,366,572 16,683,286 8,341,643 25,024,930 12,512,465 37,537,396 18,768,698 9,384,349 28,153,048 14,076,524 7,038,262 3,519,131 10,557,394 5,278,697 15,836,092 7,918,046 3,959,023 11,877,070 5,938,535 17,815,606 8,907,803 26,723,410 13,361,705 40,085,116 20,042,558 10,021,279 30,063,838 15,031,919 45,095,758 22,547,879 67,643,638 33,821,819 101,465,458 50,732,729 152,198,188 76,099,094 38,049,547

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