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Atlas › Integer Profiles › Node 8,075,480

8,075,480

23 × 5 × 7 × 151 × 191
Abundant Even Composite

8,075,480 factors as 2^3 × 5 × 7 × 151 × 191. Its 64 positive divisors give a proper-divisor sum of 12,937,000, so this integer is abundant. The Collatz stopping time is 199 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 151 × 191
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 21,012,480
Proper Divisor Sum 12,937,000
Digit Sum / Digital Root 32 (Root: 5)
Adjacent Primes #8075471 ← → #8075491

Radix Representation

Decimal 8075480
Binary 11110110011100011011000 (23 bits)
Octal 0o36634330
Hexadecimal 0x7B38D8

Divisor Catalog (60 of 64)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 151 191 280 302 382 604 755 764 955 1,057 1,208 1,337 1,510 1,528 1,910 2,114 2,674 3,020 3,820 4,228 5,285 5,348 6,040 6,685 7,640 8,456 10,570 10,696 13,370 21,140 26,740 28,841 42,280 53,480 57,682 115,364 144,205 201,887 230,728 288,410 403,774 576,820 807,548 1,009,435 1,153,640

Collatz Trajectory (199 steps to reach 1)

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

8,075,480 4,037,740 2,018,870 1,009,435 3,028,306 1,514,153 4,542,460 2,271,230 1,135,615 3,406,846 1,703,423 5,110,270 2,555,135 7,665,406 3,832,703 11,498,110 5,749,055 17,247,166 8,623,583 25,870,750 12,935,375 38,806,126 19,403,063 58,209,190 29,104,595 87,313,786 43,656,893 130,970,680 65,485,340 32,742,670 16,371,335 49,114,006 24,557,003 73,671,010 36,835,505 110,506,516 55,253,258 27,626,629 82,879,888 41,439,944 20,719,972 10,359,986 5,179,993 15,539,980 7,769,990 3,884,995 11,654,986 5,827,493 17,482,480 8,741,240 4,370,620 2,185,310 1,092,655 3,277,966 1,638,983 4,916,950 2,458,475 7,375,426 3,687,713 11,063,140

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