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Atlas › Integer Profiles › Node 8,428,288

8,428,288

28 × 11 × 41 × 73
Abundant Even Composite

8,428,288 factors as 2^8 × 11 × 41 × 73. Its 72 positive divisors give a proper-divisor sum of 10,629,968, so this integer is abundant. The Collatz stopping time is 168 steps.

Prime Factor Structure

Factorization String 2^8 × 11 × 41 × 73
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 19,058,256
Proper Divisor Sum 10,629,968
Digit Sum / Digital Root 40 (Root: 4)
Adjacent Primes #8428237 ← → #8428289

Radix Representation

Decimal 8428288
Binary 100000001001101100000000 (24 bits)
Octal 0o40115400
Hexadecimal 0x809B00

Divisor Catalog (60 of 72)

1 2 4 8 11 16 22 32 41 44 64 73 82 88 128 146 164 176 256 292 328 352 451 584 656 704 803 902 1,168 1,312 1,408 1,606 1,804 2,336 2,624 2,816 2,993 3,212 3,608 4,672 5,248 5,986 6,424 7,216 9,344 10,496 11,972 12,848 14,432 18,688 23,944 25,696 28,864 32,923 47,888 51,392 57,728 65,846 95,776 102,784

Collatz Trajectory (168 steps to reach 1)

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

8,428,288 4,214,144 2,107,072 1,053,536 526,768 263,384 131,692 65,846 32,923 98,770 49,385 148,156 74,078 37,039 111,118 55,559 166,678 83,339 250,018 125,009 375,028 187,514 93,757 281,272 140,636 70,318 35,159 105,478 52,739 158,218 79,109 237,328 118,664 59,332 29,666 14,833 44,500 22,250 11,125 33,376 16,688 8,344 4,172 2,086 1,043 3,130 1,565 4,696 2,348 1,174 587 1,762 881 2,644 1,322 661 1,984 992 496 248

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