λ
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Atlas › Integer Profiles › Node 27,754,792

27,754,792

23 × 13 × 103 × 2591
Abundant Even Composite

27,754,792 factors as 2^3 × 13 × 103 × 2591. Its 32 positive divisors give a proper-divisor sum of 28,854,488, so this integer is abundant. The Collatz stopping time is 136 steps.

Prime Factor Structure

Factorization String 2^3 × 13 × 103 × 2591
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 32
Divisor Sum (σ) 56,609,280
Proper Divisor Sum 28,854,488
Digit Sum / Digital Root 43 (Root: 7)
Adjacent Primes #27754787 ← → #27754799

Radix Representation

Decimal 27754792
Binary 1101001111000000100101000 (25 bits)
Octal 0o151700450
Hexadecimal 0x1A78128

Divisor Catalog (32)

1 2 4 8 13 26 52 103 104 206 412 824 1,339 2,591 2,678 5,182 5,356 10,364 10,712 20,728 33,683 67,366 134,732 266,873 269,464 533,746 1,067,492 2,134,984 3,469,349 6,938,698 13,877,396 27,754,792

Collatz Trajectory (136 steps to reach 1)

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

27,754,792 13,877,396 6,938,698 3,469,349 10,408,048 5,204,024 2,602,012 1,301,006 650,503 1,951,510 975,755 2,927,266 1,463,633 4,390,900 2,195,450 1,097,725 3,293,176 1,646,588 823,294 411,647 1,234,942 617,471 1,852,414 926,207 2,778,622 1,389,311 4,167,934 2,083,967 6,251,902 3,125,951 9,377,854 4,688,927 14,066,782 7,033,391 21,100,174 10,550,087 31,650,262 15,825,131 47,475,394 23,737,697 71,213,092 35,606,546 17,803,273 53,409,820 26,704,910 13,352,455 40,057,366 20,028,683 60,086,050 30,043,025 90,129,076 45,064,538 22,532,269 67,596,808 33,798,404 16,899,202 8,449,601 25,348,804 12,674,402 6,337,201

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