42,084

2² × 3² × 7 × 167

42,084 has digital root 9. The neighboring primes are 42083 and 42089; its proper-divisor sum differs from the starting integer by 38,136.

Prime Factor Structure

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

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 122,304

Proper Divisor Sum 80,220

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #42083 ← → #42089

Radix Representation

Decimal	42084
Binary	1010010001100100 (16 bits)
Octal	0o122144
Hexadecimal	0xA464

Divisor Catalog (36)

1 2 3 4 6 7 9 12 14 18 21 28 36 42 63 84 126 167 252 334 501 668 1,002 1,169 1,503 2,004 2,338 3,006 3,507 4,676 6,012 7,014 10,521 14,028 21,042 42,084

Collatz Trajectory (106 steps to reach 1)

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

42,084 21,042 10,521 31,564 15,782 7,891 23,674 11,837 35,512 17,756 8,878 4,439 13,318 6,659 19,978 9,989 29,968 14,984 7,492 3,746 1,873 5,620 2,810 1,405 4,216 2,108 1,054 527 1,582 791 2,374 1,187 3,562 1,781 5,344 2,672 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619

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