7,829,825

5² × 31 × 10103

7,829,825 factors as 5^2 × 31 × 10103. Its 12 positive divisors give a proper-divisor sum of 2,193,343, so this integer is deficient. The Collatz stopping time is 217 steps.

Prime Factor Structure

Factorization String 5^2 × 31 × 10103

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 10,023,168

Proper Divisor Sum 2,193,343

Digit Sum / Digital Root 41 (Root: 5)

Adjacent Primes #7829791 ← → #7829837

Radix Representation

Decimal	7829825
Binary	11101110111100101000001 (23 bits)
Octal	0o35674501
Hexadecimal	0x777941

Divisor Catalog (12)

1 5 25 31 155 775 10,103 50,515 252,575 313,193 1,565,965 7,829,825

Collatz Trajectory (217 steps to reach 1)

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

7,829,825 23,489,476 11,744,738 5,872,369 17,617,108 8,808,554 4,404,277 13,212,832 6,606,416 3,303,208 1,651,604 825,802 412,901 1,238,704 619,352 309,676 154,838 77,419 232,258 116,129 348,388 174,194 87,097 261,292 130,646 65,323 195,970 97,985 293,956 146,978 73,489 220,468 110,234 55,117 165,352 82,676 41,338 20,669 62,008 31,004 15,502 7,751 23,254 11,627 34,882 17,441 52,324 26,162 13,081 39,244 19,622 9,811 29,434 14,717 44,152 22,076 11,038 5,519 16,558 8,279

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