825,264

2⁴ × 3² × 11 × 521

For 825,264, the 60 positive divisors have a total of 2,524,392. Removing 825,264 leaves 1,699,128, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 11 × 521

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 2,524,392

Proper Divisor Sum 1,699,128

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #825259 ← → #825277

Radix Representation

Decimal	825264
Binary	11001001011110110000 (20 bits)
Octal	0o3113660
Hexadecimal	0xC97B0

Divisor Catalog (60)

1 2 3 4 6 8 9 11 12 16 18 22 24 33 36 44 48 66 72 88 99 132 144 176 198 264 396 521 528 792 1,042 1,563 1,584 2,084 3,126 4,168 4,689 5,731 6,252 8,336 9,378 11,462 12,504 17,193 18,756 22,924 25,008 34,386 37,512 45,848 51,579 68,772 75,024 91,696 103,158 137,544 206,316 275,088 412,632 825,264

Collatz Trajectory (82 steps to reach 1)

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

825,264 412,632 206,316 103,158 51,579 154,738 77,369 232,108 116,054 58,027 174,082 87,041 261,124 130,562 65,281 195,844 97,922 48,961 146,884 73,442 36,721 110,164 55,082 27,541 82,624 41,312 20,656 10,328 5,164 2,582 1,291 3,874 1,937 5,812 2,906 1,453 4,360 2,180 1,090 545 1,636 818 409 1,228 614 307 922 461 1,384 692 346 173 520 260 130 65 196 98 49 148

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