687,840

2⁵ × 3 × 5 × 1433

687,840 has the prime decomposition 2^5 × 3 × 5 × 1433. Its 4 distinct prime factors produce 48 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 1433

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 2,168,208

Proper Divisor Sum 1,480,368

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #687839 ← → #687847

Radix Representation

Decimal	687840
Binary	10100111111011100000 (20 bits)
Octal	0o2477340
Hexadecimal	0xA7EE0

Divisor Catalog (48)

1 2 3 4 5 6 8 10 12 15 16 20 24 30 32 40 48 60 80 96 120 160 240 480 1,433 2,866 4,299 5,732 7,165 8,598 11,464 14,330 17,196 21,495 22,928 28,660 34,392 42,990 45,856 57,320 68,784 85,980 114,640 137,568 171,960 229,280 343,920 687,840

Collatz Trajectory (105 steps to reach 1)

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

687,840 343,920 171,960 85,980 42,990 21,495 64,486 32,243 96,730 48,365 145,096 72,548 36,274 18,137 54,412 27,206 13,603 40,810 20,405 61,216 30,608 15,304 7,652 3,826 1,913 5,740 2,870 1,435 4,306 2,153 6,460 3,230 1,615 4,846 2,423 7,270 3,635 10,906 5,453 16,360 8,180 4,090 2,045 6,136 3,068 1,534 767 2,302 1,151 3,454 1,727 5,182 2,591 7,774 3,887 11,662 5,831 17,494 8,747 26,242

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