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Atlas › Integer Profiles › Node 36,348,640

36,348,640

25 × 5 × 157 × 1447
Abundant Even Composite

36,348,640 factors as 2^5 × 5 × 157 × 1447. Its 48 positive divisors give a proper-divisor sum of 50,131,712, so this integer is abundant. The Collatz stopping time is 196 steps.

Prime Factor Structure

Factorization String 2^5 × 5 × 157 × 1447
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 86,480,352
Proper Divisor Sum 50,131,712
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #36348617 ← → #36348643

Radix Representation

Decimal 36348640
Binary 10001010101010001011100000 (26 bits)
Octal 0o212521340
Hexadecimal 0x22AA2E0

Divisor Catalog (48)

1 2 4 5 8 10 16 20 32 40 80 157 160 314 628 785 1,256 1,447 1,570 2,512 2,894 3,140 5,024 5,788 6,280 7,235 11,576 12,560 14,470 23,152 25,120 28,940 46,304 57,880 115,760 227,179 231,520 454,358 908,716 1,135,895 1,817,432 2,271,790 3,634,864 4,543,580 7,269,728 9,087,160 18,174,320 36,348,640

Collatz Trajectory (196 steps to reach 1)

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

36,348,640 18,174,320 9,087,160 4,543,580 2,271,790 1,135,895 3,407,686 1,703,843 5,111,530 2,555,765 7,667,296 3,833,648 1,916,824 958,412 479,206 239,603 718,810 359,405 1,078,216 539,108 269,554 134,777 404,332 202,166 101,083 303,250 151,625 454,876 227,438 113,719 341,158 170,579 511,738 255,869 767,608 383,804 191,902 95,951 287,854 143,927 431,782 215,891 647,674 323,837 971,512 485,756 242,878 121,439 364,318 182,159 546,478 273,239 819,718 409,859 1,229,578 614,789 1,844,368 922,184 461,092 230,546

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