30,520

2³ × 5 × 7 × 109

30,520 factors as 2^3 × 5 × 7 × 109. Its 32 positive divisors give a proper-divisor sum of 48,680, so this integer is abundant. The Collatz stopping time is 178 steps.

Prime Factor Structure

Factorization String 2^3 × 5 × 7 × 109

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 32

Divisor Sum (σ) 79,200

Proper Divisor Sum 48,680

Digit Sum / Digital Root 10 (Root: 1)

Adjacent Primes #30517 ← → #30529

Radix Representation

Decimal	30520
Binary	111011100111000 (15 bits)
Octal	0o73470
Hexadecimal	0x7738

Divisor Catalog (32)

1 2 4 5 7 8 10 14 20 28 35 40 56 70 109 140 218 280 436 545 763 872 1,090 1,526 2,180 3,052 3,815 4,360 6,104 7,630 15,260 30,520

Collatz Trajectory (178 steps to reach 1)

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

30,520 15,260 7,630 3,815 11,446 5,723 17,170 8,585 25,756 12,878 6,439 19,318 9,659 28,978 14,489 43,468 21,734 10,867 32,602 16,301 48,904 24,452 12,226 6,113 18,340 9,170 4,585 13,756 6,878 3,439 10,318 5,159 15,478 7,739 23,218 11,609 34,828 17,414 8,707 26,122 13,061 39,184 19,592 9,796 4,898 2,449 7,348 3,674 1,837 5,512 2,756 1,378 689 2,068 1,034 517 1,552 776 388 194

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