6,048,000

2⁸ × 3³ × 5³ × 7

6,048,000 has digital root 9. The neighboring primes are 6047999 and 6048013; its proper-divisor sum differs from the starting integer by 13,413,120.

Prime Factor Structure

Factorization String 2^8 × 3^3 × 5^3 × 7

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 288

Divisor Sum (σ) 25,509,120

Proper Divisor Sum 19,461,120

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #6047999 ← → #6048013

Radix Representation

Decimal	6048000
Binary	10111000100100100000000 (23 bits)
Octal	0o27044400
Hexadecimal	0x5C4900

Divisor Catalog (60 of 288)

1 2 3 4 5 6 7 8 9 10 12 14 15 16 18 20 21 24 25 27 28 30 32 35 36 40 42 45 48 50 54 56 60 63 64 70 72 75 80 84 90 96 100 105 108 112 120 125 126 128 135 140 144 150 160 168 175 180 189 192

Collatz Trajectory (90 steps to reach 1)

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

6,048,000 3,024,000 1,512,000 756,000 378,000 189,000 94,500 47,250 23,625 70,876 35,438 17,719 53,158 26,579 79,738 39,869 119,608 59,804 29,902 14,951 44,854 22,427 67,282 33,641 100,924 50,462 25,231 75,694 37,847 113,542 56,771 170,314 85,157 255,472 127,736 63,868 31,934 15,967 47,902 23,951 71,854 35,927 107,782 53,891 161,674 80,837 242,512 121,256 60,628 30,314 15,157 45,472 22,736 11,368 5,684 2,842 1,421 4,264 2,132 1,066

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