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Atlas › Integer Profiles › Node 27,442,000

27,442,000

24 × 53 × 13721
Abundant Even Composite

27,442,000 factors as 2^4 × 5^3 × 13721. Its 40 positive divisors give a proper-divisor sum of 38,917,592, so this integer is abundant. The Collatz stopping time is 79 steps.

Prime Factor Structure

Factorization String 2^4 × 5^3 × 13721
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 66,359,592
Proper Divisor Sum 38,917,592
Digit Sum / Digital Root 19 (Root: 1)
Adjacent Primes #27441991 ← → #27442001

Radix Representation

Decimal 27442000
Binary 1101000101011101101010000 (25 bits)
Octal 0o150535520
Hexadecimal 0x1A2BB50

Divisor Catalog (40)

1 2 4 5 8 10 16 20 25 40 50 80 100 125 200 250 400 500 1,000 2,000 13,721 27,442 54,884 68,605 109,768 137,210 219,536 274,420 343,025 548,840 686,050 1,097,680 1,372,100 1,715,125 2,744,200 3,430,250 5,488,400 6,860,500 13,721,000 27,442,000

Collatz Trajectory (79 steps to reach 1)

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

27,442,000 13,721,000 6,860,500 3,430,250 1,715,125 5,145,376 2,572,688 1,286,344 643,172 321,586 160,793 482,380 241,190 120,595 361,786 180,893 542,680 271,340 135,670 67,835 203,506 101,753 305,260 152,630 76,315 228,946 114,473 343,420 171,710 85,855 257,566 128,783 386,350 193,175 579,526 289,763 869,290 434,645 1,303,936 651,968 325,984 162,992 81,496 40,748 20,374 10,187 30,562 15,281 45,844 22,922 11,461 34,384 17,192 8,596 4,298 2,149 6,448 3,224 1,612 806

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