344,964

2² × 3 × 17 × 19 × 89

344,964 factors as 2^2 × 3 × 17 × 19 × 89. Its 48 positive divisors give a proper-divisor sum of 562,236, so this integer is abundant. The Collatz stopping time is 91 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 17 × 19 × 89

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 907,200

Proper Divisor Sum 562,236

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #344963 ← → #344969

Radix Representation

Decimal	344964
Binary	1010100001110000100 (19 bits)
Octal	0o1241604
Hexadecimal	0x54384

Divisor Catalog (48)

1 2 3 4 6 12 17 19 34 38 51 57 68 76 89 102 114 178 204 228 267 323 356 534 646 969 1,068 1,292 1,513 1,691 1,938 3,026 3,382 3,876 4,539 5,073 6,052 6,764 9,078 10,146 18,156 20,292 28,747 57,494 86,241 114,988 172,482 344,964

Collatz Trajectory (91 steps to reach 1)

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

344,964 172,482 86,241 258,724 129,362 64,681 194,044 97,022 48,511 145,534 72,767 218,302 109,151 327,454 163,727 491,182 245,591 736,774 368,387 1,105,162 552,581 1,657,744 828,872 414,436 207,218 103,609 310,828 155,414 77,707 233,122 116,561 349,684 174,842 87,421 262,264 131,132 65,566 32,783 98,350 49,175 147,526 73,763 221,290 110,645 331,936 165,968 82,984 41,492 20,746 10,373 31,120 15,560 7,780 3,890 1,945 5,836 2,918 1,459 4,378 2,189

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