500,360

2³ × 5 × 7 × 1787

500,360 factors as 2^3 × 5 × 7 × 1787. Its 32 positive divisors give a proper-divisor sum of 787,000, so this integer is abundant. The Collatz stopping time is 138 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 1787

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 1,287,360

Proper Divisor Sum 787,000

Digit Sum / Digital Root 14 (Root: 5)

Adjacent Primes #500341 ← → #500363

Radix Representation

Decimal	500360
Binary	1111010001010001000 (19 bits)
Octal	0o1721210
Hexadecimal	0x7A288

Divisor Catalog (32)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 140 280 1,787 3,574 7,148 8,935 12,509 14,296 17,870 25,018 35,740 50,036 62,545 71,480 100,072 125,090 250,180 500,360

Collatz Trajectory (138 steps to reach 1)

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

500,360 250,180 125,090 62,545 187,636 93,818 46,909 140,728 70,364 35,182 17,591 52,774 26,387 79,162 39,581 118,744 59,372 29,686 14,843 44,530 22,265 66,796 33,398 16,699 50,098 25,049 75,148 37,574 18,787 56,362 28,181 84,544 42,272 21,136 10,568 5,284 2,642 1,321 3,964 1,982 991 2,974 1,487 4,462 2,231 6,694 3,347 10,042 5,021 15,064 7,532 3,766 1,883 5,650 2,825 8,476 4,238 2,119 6,358 3,179

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