420,180

2² × 3 × 5 × 47 × 149

420,180 has the prime decomposition 2^2 × 3 × 5 × 47 × 149. Its 5 distinct prime factors produce 48 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 47 × 149

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,209,600

Proper Divisor Sum 789,420

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #420163 ← → #420191

Radix Representation

Decimal	420180
Binary	1100110100101010100 (19 bits)
Octal	0o1464524
Hexadecimal	0x66954

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 30 47 60 94 141 149 188 235 282 298 447 470 564 596 705 745 894 940 1,410 1,490 1,788 2,235 2,820 2,980 4,470 7,003 8,940 14,006 21,009 28,012 35,015 42,018 70,030 84,036 105,045 140,060 210,090 420,180

Collatz Trajectory (81 steps to reach 1)

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

420,180 210,090 105,045 315,136 157,568 78,784 39,392 19,696 9,848 4,924 2,462 1,231 3,694 1,847 5,542 2,771 8,314 4,157 12,472 6,236 3,118 1,559 4,678 2,339 7,018 3,509 10,528 5,264 2,632 1,316 658 329 988 494 247 742 371 1,114 557 1,672 836 418 209 628 314 157 472 236 118 59 178 89 268 134 67 202 101 304 152 76

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