417,225

3 × 5² × 5563

417,225 factors as 3 × 5^2 × 5563. Its 12 positive divisors give a proper-divisor sum of 272,711, so this integer is deficient. The Collatz stopping time is 86 steps.

Prime Factor Structure

Factorization String 3 × 5^2 × 5563

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 689,936

Proper Divisor Sum 272,711

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #417217 ← → #417227

Radix Representation

Decimal	417225
Binary	1100101110111001001 (19 bits)
Octal	0o1456711
Hexadecimal	0x65DC9

Divisor Catalog (12)

1 3 5 15 25 75 5,563 16,689 27,815 83,445 139,075 417,225

Collatz Trajectory (86 steps to reach 1)

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

417,225 1,251,676 625,838 312,919 938,758 469,379 1,408,138 704,069 2,112,208 1,056,104 528,052 264,026 132,013 396,040 198,020 99,010 49,505 148,516 74,258 37,129 111,388 55,694 27,847 83,542 41,771 125,314 62,657 187,972 93,986 46,993 140,980 70,490 35,245 105,736 52,868 26,434 13,217 39,652 19,826 9,913 29,740 14,870 7,435 22,306 11,153 33,460 16,730 8,365 25,096 12,548 6,274 3,137 9,412 4,706 2,353 7,060 3,530 1,765 5,296 2,648

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