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Atlas › Integer Profiles › Node 2,824,136

2,824,136

23 × 7 × 29 × 37 × 47
Abundant Even Composite

2,824,136 factors as 2^3 × 7 × 29 × 37 × 47. Its 64 positive divisors give a proper-divisor sum of 3,742,264, so this integer is abundant. The Collatz stopping time is 107 steps.

Prime Factor Structure

Factorization String 2^3 × 7 × 29 × 37 × 47
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 6,566,400
Proper Divisor Sum 3,742,264
Digit Sum / Digital Root 26 (Root: 8)
Adjacent Primes #2824127 ← → #2824139

Radix Representation

Decimal 2824136
Binary 1010110001011111001000 (22 bits)
Octal 0o12613710
Hexadecimal 0x2B17C8

Divisor Catalog (60 of 64)

1 2 4 7 8 14 28 29 37 47 56 58 74 94 116 148 188 203 232 259 296 329 376 406 518 658 812 1,036 1,073 1,316 1,363 1,624 1,739 2,072 2,146 2,632 2,726 3,478 4,292 5,452 6,956 7,511 8,584 9,541 10,904 12,173 13,912 15,022 19,082 24,346 30,044 38,164 48,692 50,431 60,088 76,328 97,384 100,862 201,724 353,017

Collatz Trajectory (107 steps to reach 1)

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

2,824,136 1,412,068 706,034 353,017 1,059,052 529,526 264,763 794,290 397,145 1,191,436 595,718 297,859 893,578 446,789 1,340,368 670,184 335,092 167,546 83,773 251,320 125,660 62,830 31,415 94,246 47,123 141,370 70,685 212,056 106,028 53,014 26,507 79,522 39,761 119,284 59,642 29,821 89,464 44,732 22,366 11,183 33,550 16,775 50,326 25,163 75,490 37,745 113,236 56,618 28,309 84,928 42,464 21,232 10,616 5,308 2,654 1,327 3,982 1,991 5,974 2,987

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