433,888

2⁵ × 7 × 13 × 149

433,888 factors as 2^5 × 7 × 13 × 149. Its 48 positive divisors give a proper-divisor sum of 624,512, so this integer is abundant. The Collatz stopping time is 94 steps.

Prime Factor Structure

Factorization String 2^5 × 7 × 13 × 149

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 1,058,400

Proper Divisor Sum 624,512

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #433883 ← → #433889

Radix Representation

Decimal	433888
Binary	1101001111011100000 (19 bits)
Octal	0o1517340
Hexadecimal	0x69EE0

Divisor Catalog (48)

1 2 4 7 8 13 14 16 26 28 32 52 56 91 104 112 149 182 208 224 298 364 416 596 728 1,043 1,192 1,456 1,937 2,086 2,384 2,912 3,874 4,172 4,768 7,748 8,344 13,559 15,496 16,688 27,118 30,992 33,376 54,236 61,984 108,472 216,944 433,888

Collatz Trajectory (94 steps to reach 1)

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

433,888 216,944 108,472 54,236 27,118 13,559 40,678 20,339 61,018 30,509 91,528 45,764 22,882 11,441 34,324 17,162 8,581 25,744 12,872 6,436 3,218 1,609 4,828 2,414 1,207 3,622 1,811 5,434 2,717 8,152 4,076 2,038 1,019 3,058 1,529 4,588 2,294 1,147 3,442 1,721 5,164 2,582 1,291 3,874 1,937 5,812 2,906 1,453 4,360 2,180 1,090 545 1,636 818 409 1,228 614 307 922 461

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