42,105

3 × 5 × 7 × 401

42,105 has the prime decomposition 3 × 5 × 7 × 401. Its 4 distinct prime factors produce 16 positive divisors.

Prime Factor Structure

Factorization String 3 × 5 × 7 × 401

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 77,184

Proper Divisor Sum 35,079

Digit Sum / Digital Root 12 (Root: 3)

Adjacent Primes #42101 ← → #42131

Radix Representation

Decimal	42105
Binary	1010010001111001 (16 bits)
Octal	0o122171
Hexadecimal	0xA479

Divisor Catalog (16)

1 3 5 7 15 21 35 105 401 1,203 2,005 2,807 6,015 8,421 14,035 42,105

Collatz Trajectory (119 steps to reach 1)

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

42,105 126,316 63,158 31,579 94,738 47,369 142,108 71,054 35,527 106,582 53,291 159,874 79,937 239,812 119,906 59,953 179,860 89,930 44,965 134,896 67,448 33,724 16,862 8,431 25,294 12,647 37,942 18,971 56,914 28,457 85,372 42,686 21,343 64,030 32,015 96,046 48,023 144,070 72,035 216,106 108,053 324,160 162,080 81,040 40,520 20,260 10,130 5,065 15,196 7,598 3,799 11,398 5,699 17,098 8,549 25,648 12,824 6,412 3,206 1,603

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