3,507,000

2³ × 3 × 5³ × 7 × 167

3,507,000 has the prime decomposition 2^3 × 3 × 5^3 × 7 × 167. Its 5 distinct prime factors produce 128 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3 × 5^3 × 7 × 167

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 128

Divisor Sum (σ) 12,579,840

Proper Divisor Sum 9,072,840

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #3506989 ← → #3507029

Radix Representation

Decimal	3507000
Binary	1101011000001100111000 (22 bits)
Octal	0o15301470
Hexadecimal	0x358338

Divisor Catalog (60 of 128)

1 2 3 4 5 6 7 8 10 12 14 15 20 21 24 25 28 30 35 40 42 50 56 60 70 75 84 100 105 120 125 140 150 167 168 175 200 210 250 280 300 334 350 375 420 500 501 525 600 668 700 750 835 840 875 1,000 1,002 1,050 1,169 1,336

Collatz Trajectory (190 steps to reach 1)

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

3,507,000 1,753,500 876,750 438,375 1,315,126 657,563 1,972,690 986,345 2,959,036 1,479,518 739,759 2,219,278 1,109,639 3,328,918 1,664,459 4,993,378 2,496,689 7,490,068 3,745,034 1,872,517 5,617,552 2,808,776 1,404,388 702,194 351,097 1,053,292 526,646 263,323 789,970 394,985 1,184,956 592,478 296,239 888,718 444,359 1,333,078 666,539 1,999,618 999,809 2,999,428 1,499,714 749,857 2,249,572 1,124,786 562,393 1,687,180 843,590 421,795 1,265,386 632,693 1,898,080 949,040 474,520 237,260 118,630 59,315 177,946 88,973 266,920 133,460

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