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Atlas › Integer Profiles › Node 10,240,720

10,240,720

24 × 5 × 7 × 18287
Abundant Even Composite

10,240,720 factors as 2^4 × 5 × 7 × 18287. Its 40 positive divisors give a proper-divisor sum of 16,971,824, so this integer is abundant. The Collatz stopping time is 101 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 18287
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 27,212,544
Proper Divisor Sum 16,971,824
Digit Sum / Digital Root 16 (Root: 7)
Adjacent Primes #10240709 ← → #10240723

Radix Representation

Decimal 10240720
Binary 100111000100001011010000 (24 bits)
Octal 0o47041320
Hexadecimal 0x9C42D0

Divisor Catalog (40)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 280 560 18,287 36,574 73,148 91,435 128,009 146,296 182,870 256,018 292,592 365,740 512,036 640,045 731,480 1,024,072 1,280,090 1,462,960 2,048,144 2,560,180 5,120,360 10,240,720

Collatz Trajectory (101 steps to reach 1)

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

10,240,720 5,120,360 2,560,180 1,280,090 640,045 1,920,136 960,068 480,034 240,017 720,052 360,026 180,013 540,040 270,020 135,010 67,505 202,516 101,258 50,629 151,888 75,944 37,972 18,986 9,493 28,480 14,240 7,120 3,560 1,780 890 445 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644 1,822

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