827,762

2 × 13² × 31 × 79

827,762 is even and not a perfect square. Its factorization is 2 × 13^2 × 31 × 79 and its 24 divisors sum to 1,405,440.

Prime Factor Structure

Factorization String 2 × 13^2 × 31 × 79

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,405,440

Proper Divisor Sum 577,678

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #827741 ← → #827767

Radix Representation

Decimal	827762
Binary	11001010000101110010 (20 bits)
Octal	0o3120562
Hexadecimal	0xCA172

Divisor Catalog (24)

1 2 13 26 31 62 79 158 169 338 403 806 1,027 2,054 2,449 4,898 5,239 10,478 13,351 26,702 31,837 63,674 413,881 827,762

Collatz Trajectory (87 steps to reach 1)

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

827,762 413,881 1,241,644 620,822 310,411 931,234 465,617 1,396,852 698,426 349,213 1,047,640 523,820 261,910 130,955 392,866 196,433 589,300 294,650 147,325 441,976 220,988 110,494 55,247 165,742 82,871 248,614 124,307 372,922 186,461 559,384 279,692 139,846 69,923 209,770 104,885 314,656 157,328 78,664 39,332 19,666 9,833 29,500 14,750 7,375 22,126 11,063 33,190 16,595 49,786 24,893 74,680 37,340 18,670 9,335 28,006 14,003 42,010 21,005 63,016 31,508

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