7,722,825

3 × 5² × 11² × 23 × 37

7,722,825 has the prime decomposition 3 × 5^2 × 11^2 × 23 × 37. Its 5 distinct prime factors produce 72 positive divisors.

Prime Factor Structure

Factorization String 3 × 5^2 × 11^2 × 23 × 37

Distinct Prime Factors 5

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 15,040,704

Proper Divisor Sum 7,317,879

Digit Sum / Digital Root 33 (Root: 6)

Adjacent Primes #7722823 ← → #7722829

Radix Representation

Decimal	7722825
Binary	11101011101011101001001 (23 bits)
Octal	0o35353511
Hexadecimal	0x75D749

Divisor Catalog (60 of 72)

1 3 5 11 15 23 25 33 37 55 69 75 111 115 121 165 185 253 275 345 363 407 555 575 605 759 825 851 925 1,221 1,265 1,725 1,815 2,035 2,553 2,775 2,783 3,025 3,795 4,255 4,477 6,105 6,325 8,349 9,075 9,361 10,175 12,765 13,431 13,915 18,975 21,275 22,385 28,083 30,525 41,745 46,805 63,825 67,155 69,575

Collatz Trajectory (72 steps to reach 1)

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

7,722,825 23,168,476 11,584,238 5,792,119 17,376,358 8,688,179 26,064,538 13,032,269 39,096,808 19,548,404 9,774,202 4,887,101 14,661,304 7,330,652 3,665,326 1,832,663 5,497,990 2,748,995 8,246,986 4,123,493 12,370,480 6,185,240 3,092,620 1,546,310 773,155 2,319,466 1,159,733 3,479,200 1,739,600 869,800 434,900 217,450 108,725 326,176 163,088 81,544 40,772 20,386 10,193 30,580 15,290 7,645 22,936 11,468 5,734 2,867 8,602 4,301 12,904 6,452 3,226 1,613 4,840 2,420 1,210 605 1,816 908 454 227

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