613,350

2 × 3² × 5² × 29 × 47

613,350 has the prime decomposition 2 × 3^2 × 5^2 × 29 × 47. Its 5 distinct prime factors produce 72 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^2 × 5^2 × 29 × 47

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 1,740,960

Proper Divisor Sum 1,127,610

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #613337 ← → #613357

Radix Representation

Decimal	613350
Binary	10010101101111100110 (20 bits)
Octal	0o2255746
Hexadecimal	0x95BE6

Divisor Catalog (60 of 72)

1 2 3 5 6 9 10 15 18 25 29 30 45 47 50 58 75 87 90 94 141 145 150 174 225 235 261 282 290 423 435 450 470 522 705 725 846 870 1,175 1,305 1,363 1,410 1,450 2,115 2,175 2,350 2,610 2,726 3,525 4,089 4,230 4,350 6,525 6,815 7,050 8,178 10,575 12,267 13,050 13,630

Collatz Trajectory (141 steps to reach 1)

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

613,350 306,675 920,026 460,013 1,380,040 690,020 345,010 172,505 517,516 258,758 129,379 388,138 194,069 582,208 291,104 145,552 72,776 36,388 18,194 9,097 27,292 13,646 6,823 20,470 10,235 30,706 15,353 46,060 23,030 11,515 34,546 17,273 51,820 25,910 12,955 38,866 19,433 58,300 29,150 14,575 43,726 21,863 65,590 32,795 98,386 49,193 147,580 73,790 36,895 110,686 55,343 166,030 83,015 249,046 124,523 373,570 186,785 560,356 280,178 140,089

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