34,720

2⁵ × 5 × 7 × 31

34,720 has digital root 7. The neighboring primes are 34703 and 34721; its proper-divisor sum differs from the starting integer by 27,328.

Prime Factor Structure

Factorization String 2^5 × 5 × 7 × 31

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 96,768

Proper Divisor Sum 62,048

Digit Sum / Digital Root 16 (Root: 7)

Adjacent Primes #34703 ← → #34721

Radix Representation

Decimal	34720
Binary	1000011110100000 (16 bits)
Octal	0o103640
Hexadecimal	0x87A0

Divisor Catalog (48)

1 2 4 5 7 8 10 14 16 20 28 31 32 35 40 56 62 70 80 112 124 140 155 160 217 224 248 280 310 434 496 560 620 868 992 1,085 1,120 1,240 1,736 2,170 2,480 3,472 4,340 4,960 6,944 8,680 17,360 34,720

Collatz Trajectory (49 steps to reach 1)

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

34,720 17,360 8,680 4,340 2,170 1,085 3,256 1,628 814 407 1,222 611 1,834 917 2,752 1,376 688 344 172 86 43 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1

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