λ
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Atlas › Integer Profiles › Node 961,002

961,002

2 × 32 × 7 × 29 × 263
Abundant Even Composite

961,002 factors as 2 × 3^2 × 7 × 29 × 263. Its 48 positive divisors give a proper-divisor sum of 1,510,038, so this integer is abundant. The Collatz stopping time is 108 steps.

Prime Factor Structure

Factorization String 2 × 3^2 × 7 × 29 × 263
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 2,471,040
Proper Divisor Sum 1,510,038
Digit Sum / Digital Root 18 (Root: 9)
Adjacent Primes #960991 ← → #961003

Radix Representation

Decimal 961002
Binary 11101010100111101010 (20 bits)
Octal 0o3524752
Hexadecimal 0xEA9EA

Divisor Catalog (48)

1 2 3 6 7 9 14 18 21 29 42 58 63 87 126 174 203 261 263 406 522 526 609 789 1,218 1,578 1,827 1,841 2,367 3,654 3,682 4,734 5,523 7,627 11,046 15,254 16,569 22,881 33,138 45,762 53,389 68,643 106,778 137,286 160,167 320,334 480,501 961,002

Collatz Trajectory (108 steps to reach 1)

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

961,002 480,501 1,441,504 720,752 360,376 180,188 90,094 45,047 135,142 67,571 202,714 101,357 304,072 152,036 76,018 38,009 114,028 57,014 28,507 85,522 42,761 128,284 64,142 32,071 96,214 48,107 144,322 72,161 216,484 108,242 54,121 162,364 81,182 40,591 121,774 60,887 182,662 91,331 273,994 136,997 410,992 205,496 102,748 51,374 25,687 77,062 38,531 115,594 57,797 173,392 86,696 43,348 21,674 10,837 32,512 16,256 8,128 4,064 2,032 1,016

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