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Atlas › Integer Profiles › Node 10,072,640

10,072,640

26 × 5 × 31477
Abundant Even Composite

10,072,640 factors as 2^6 × 5 × 31477. Its 28 positive divisors give a proper-divisor sum of 13,913,596, so this integer is abundant. The Collatz stopping time is 176 steps.

Prime Factor Structure

Factorization String 2^6 × 5 × 31477
Distinct Prime Factors 3
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 28
Divisor Sum (σ) 23,986,236
Proper Divisor Sum 13,913,596
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #10072639 ← → #10072663

Radix Representation

Decimal 10072640
Binary 100110011011001001000000 (24 bits)
Octal 0o46331100
Hexadecimal 0x99B240

Divisor Catalog (28)

1 2 4 5 8 10 16 20 32 40 64 80 160 320 31,477 62,954 125,908 157,385 251,816 314,770 503,632 629,540 1,007,264 1,259,080 2,014,528 2,518,160 5,036,320 10,072,640

Collatz Trajectory (176 steps to reach 1)

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

10,072,640 5,036,320 2,518,160 1,259,080 629,540 314,770 157,385 472,156 236,078 118,039 354,118 177,059 531,178 265,589 796,768 398,384 199,192 99,596 49,798 24,899 74,698 37,349 112,048 56,024 28,012 14,006 7,003 21,010 10,505 31,516 15,758 7,879 23,638 11,819 35,458 17,729 53,188 26,594 13,297 39,892 19,946 9,973 29,920 14,960 7,480 3,740 1,870 935 2,806 1,403 4,210 2,105 6,316 3,158 1,579 4,738 2,369 7,108 3,554 1,777

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