586,768

2⁴ × 7 × 13² × 31

586,768 factors as 2^4 × 7 × 13^2 × 31. Its 60 positive divisors give a proper-divisor sum of 865,520, so this integer is abundant. The Collatz stopping time is 159 steps.

Prime Factor Structure

Factorization String 2^4 × 7 × 13^2 × 31

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 1,452,288

Proper Divisor Sum 865,520

Digit Sum / Digital Root 40 (Root: 4)

Adjacent Primes #586741 ← → #586769

Radix Representation

Decimal	586768
Binary	10001111010000010000 (20 bits)
Octal	0o2172020
Hexadecimal	0x8F410

Divisor Catalog (60)

1 2 4 7 8 13 14 16 26 28 31 52 56 62 91 104 112 124 169 182 208 217 248 338 364 403 434 496 676 728 806 868 1,183 1,352 1,456 1,612 1,736 2,366 2,704 2,821 3,224 3,472 4,732 5,239 5,642 6,448 9,464 10,478 11,284 18,928 20,956 22,568 36,673 41,912 45,136 73,346 83,824 146,692 293,384 586,768

Collatz Trajectory (159 steps to reach 1)

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

586,768 293,384 146,692 73,346 36,673 110,020 55,010 27,505 82,516 41,258 20,629 61,888 30,944 15,472 7,736 3,868 1,934 967 2,902 1,451 4,354 2,177 6,532 3,266 1,633 4,900 2,450 1,225 3,676 1,838 919 2,758 1,379 4,138 2,069 6,208 3,104 1,552 776 388 194 97 292 146 73 220 110 55 166 83 250 125 376 188 94 47 142 71 214 107

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