1,461,600

2⁵ × 3² × 5² × 7 × 29

For 1,461,600, the 216 positive divisors have a total of 6,093,360. Removing 1,461,600 leaves 4,631,760, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^5 × 3^2 × 5^2 × 7 × 29

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 216

Divisor Sum (σ) 6,093,360

Proper Divisor Sum 4,631,760

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #1461599 ← → #1461601

Radix Representation

Decimal	1461600
Binary	101100100110101100000 (21 bits)
Octal	0o5446540
Hexadecimal	0x164D60

Divisor Catalog (60 of 216)

1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 28 29 30 32 35 36 40 42 45 48 50 56 58 60 63 70 72 75 80 84 87 90 96 100 105 112 116 120 126 140 144 145 150 160 168 174 175 180 200 203 210

Collatz Trajectory (62 steps to reach 1)

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

1,461,600 730,800 365,400 182,700 91,350 45,675 137,026 68,513 205,540 102,770 51,385 154,156 77,078 38,539 115,618 57,809 173,428 86,714 43,357 130,072 65,036 32,518 16,259 48,778 24,389 73,168 36,584 18,292 9,146 4,573 13,720 6,860 3,430 1,715 5,146 2,573 7,720 3,860 1,930 965 2,896 1,448 724 362 181 544 272 136 68 34 17 52 26 13 40 20 10 5 16 8

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