498,480

2⁴ × 3 × 5 × 31 × 67

498,480 has the prime decomposition 2^4 × 3 × 5 × 31 × 67. Its 5 distinct prime factors produce 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3 × 5 × 31 × 67

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 1,618,944

Proper Divisor Sum 1,120,464

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #498469 ← → #498493

Radix Representation

Decimal	498480
Binary	1111001101100110000 (19 bits)
Octal	0o1715460
Hexadecimal	0x79B30

Divisor Catalog (60 of 80)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 31 40 48 60 62 67 80 93 120 124 134 155 186 201 240 248 268 310 335 372 402 465 496 536 620 670 744 804 930 1,005 1,072 1,240 1,340 1,488 1,608 1,860 2,010 2,077 2,480 2,680 3,216 3,720 4,020 4,154 5,360 6,231

Collatz Trajectory (89 steps to reach 1)

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

498,480 249,240 124,620 62,310 31,155 93,466 46,733 140,200 70,100 35,050 17,525 52,576 26,288 13,144 6,572 3,286 1,643 4,930 2,465 7,396 3,698 1,849 5,548 2,774 1,387 4,162 2,081 6,244 3,122 1,561 4,684 2,342 1,171 3,514 1,757 5,272 2,636 1,318 659 1,978 989 2,968 1,484 742 371 1,114 557 1,672 836 418 209 628 314 157 472 236 118 59 178 89

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