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Atlas › Integer Profiles › Node 7,200,320

7,200,320

26 × 5 × 22501
Abundant Even Composite

7,200,320 factors as 2^6 × 5 × 22501. Its 28 positive divisors give a proper-divisor sum of 9,946,204, so this integer is abundant. The Collatz stopping time is 191 steps.

Prime Factor Structure

Factorization String 2^6 × 5 × 22501
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 17,146,524
Proper Divisor Sum 9,946,204
Digit Sum / Digital Root 14 (Root: 5)
Adjacent Primes #7200317 ← → #7200331

Radix Representation

Decimal 7200320
Binary 11011011101111001000000 (23 bits)
Octal 0o33357100
Hexadecimal 0x6DDE40

Divisor Catalog (28)

1 2 4 5 8 10 16 20 32 40 64 80 160 320 22,501 45,002 90,004 112,505 180,008 225,010 360,016 450,020 720,032 900,040 1,440,064 1,800,080 3,600,160 7,200,320

Collatz Trajectory (191 steps to reach 1)

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

7,200,320 3,600,160 1,800,080 900,040 450,020 225,010 112,505 337,516 168,758 84,379 253,138 126,569 379,708 189,854 94,927 284,782 142,391 427,174 213,587 640,762 320,381 961,144 480,572 240,286 120,143 360,430 180,215 540,646 270,323 810,970 405,485 1,216,456 608,228 304,114 152,057 456,172 228,086 114,043 342,130 171,065 513,196 256,598 128,299 384,898 192,449 577,348 288,674 144,337 433,012 216,506 108,253 324,760 162,380 81,190 40,595 121,786 60,893 182,680 91,340 45,670

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