684,075

3 × 5² × 7 × 1303

For 684,075, the 24 positive divisors have a total of 1,293,568. Removing 684,075 leaves 609,493, which gives the deficient classification.

Prime Factor Structure

Factorization String 3 × 5^2 × 7 × 1303

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 1,293,568

Proper Divisor Sum 609,493

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #684053 ← → #684091

Radix Representation

Decimal	684075
Binary	10100111000000101011 (20 bits)
Octal	0o2470053
Hexadecimal	0xA702B

Divisor Catalog (24)

1 3 5 7 15 21 25 35 75 105 175 525 1,303 3,909 6,515 9,121 19,545 27,363 32,575 45,605 97,725 136,815 228,025 684,075

Collatz Trajectory (105 steps to reach 1)

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

684,075 2,052,226 1,026,113 3,078,340 1,539,170 769,585 2,308,756 1,154,378 577,189 1,731,568 865,784 432,892 216,446 108,223 324,670 162,335 487,006 243,503 730,510 365,255 1,095,766 547,883 1,643,650 821,825 2,465,476 1,232,738 616,369 1,849,108 924,554 462,277 1,386,832 693,416 346,708 173,354 86,677 260,032 130,016 65,008 32,504 16,252 8,126 4,063 12,190 6,095 18,286 9,143 27,430 13,715 41,146 20,573 61,720 30,860 15,430 7,715 23,146 11,573 34,720 17,360 8,680 4,340

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