λ
Math Directory

585,760

25 × 5 × 7 × 523
Abundant Even Composite

585,760 factors as 2^5 × 5 × 7 × 523. Its 48 positive divisors give a proper-divisor sum of 998,816, so this integer is abundant. The Collatz stopping time is 66 steps.

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Prime Factor Structure

Factorization String 2^5 × 5 × 7 × 523
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 1,584,576
Proper Divisor Sum 998,816
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #585757 ← → #585779

Radix Representation

Decimal 585760
Binary 10001111000000100000 (20 bits)
Octal 0o2170040
Hexadecimal 0x8F020

Divisor Catalog (5 of 48)

1 2 4 5 7

Collatz Trajectory (66 steps to reach 1)

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

Showing the first 5 trajectory entries; the stopping-time total above is unchanged.

585,760 292,880 146,440 73,220 36,610

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