46,500

2² × 3 × 5³ × 31

For 46,500, the 48 positive divisors have a total of 139,776. Removing 46,500 leaves 93,276, which gives the abundant classification.

Prime Factor Structure

Factorization String 2^2 × 3 × 5^3 × 31

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 139,776

Proper Divisor Sum 93,276

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #46499 ← → #46507

Radix Representation

Decimal	46500
Binary	1011010110100100 (16 bits)
Octal	0o132644
Hexadecimal	0xB5A4

Divisor Catalog (48)

1 2 3 4 5 6 10 12 15 20 25 30 31 50 60 62 75 93 100 124 125 150 155 186 250 300 310 372 375 465 500 620 750 775 930 1,500 1,550 1,860 2,325 3,100 3,875 4,650 7,750 9,300 11,625 15,500 23,250 46,500

Collatz Trajectory (176 steps to reach 1)

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

46,500 23,250 11,625 34,876 17,438 8,719 26,158 13,079 39,238 19,619 58,858 29,429 88,288 44,144 22,072 11,036 5,518 2,759 8,278 4,139 12,418 6,209 18,628 9,314 4,657 13,972 6,986 3,493 10,480 5,240 2,620 1,310 655 1,966 983 2,950 1,475 4,426 2,213 6,640 3,320 1,660 830 415 1,246 623 1,870 935 2,806 1,403 4,210 2,105 6,316 3,158 1,579 4,738 2,369 7,108 3,554 1,777

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