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Atlas › Integer Profiles › Node 828,880

828,880

24 × 5 × 13 × 797
Abundant Even Composite

828,880 factors as 2^4 × 5 × 13 × 797. Its 40 positive divisors give a proper-divisor sum of 1,249,112, so this integer is abundant. The Collatz stopping time is 56 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 13 × 797
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 40
Divisor Sum (σ) 2,077,992
Proper Divisor Sum 1,249,112
Digit Sum / Digital Root 34 (Root: 7)
Adjacent Primes #828871 ← → #828881

Radix Representation

Decimal 828880
Binary 11001010010111010000 (20 bits)
Octal 0o3122720
Hexadecimal 0xCA5D0

Divisor Catalog (40)

1 2 4 5 8 10 13 16 20 26 40 52 65 80 104 130 208 260 520 797 1,040 1,594 3,188 3,985 6,376 7,970 10,361 12,752 15,940 20,722 31,880 41,444 51,805 63,760 82,888 103,610 165,776 207,220 414,440 828,880

Collatz Trajectory (56 steps to reach 1)

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

828,880 414,440 207,220 103,610 51,805 155,416 77,708 38,854 19,427 58,282 29,141 87,424 43,712 21,856 10,928 5,464 2,732 1,366 683 2,050 1,025 3,076 1,538 769 2,308 1,154 577 1,732 866 433 1,300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

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