7,827,609

3 × 37 × 97 × 727

7,827,609 factors as 3 × 37 × 97 × 727. Its 16 positive divisors give a proper-divisor sum of 3,016,679, so this integer is deficient. The Collatz stopping time is 173 steps.

Prime Factor Structure

Factorization String 3 × 37 × 97 × 727

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 16

Divisor Sum (σ) 10,844,288

Proper Divisor Sum 3,016,679

Digit Sum / Digital Root 39 (Root: 3)

Adjacent Primes #7827607 ← → #7827619

Radix Representation

Decimal	7827609
Binary	11101110111000010011001 (23 bits)
Octal	0o35670231
Hexadecimal	0x777099

Divisor Catalog (16)

1 3 37 97 111 291 727 2,181 3,589 10,767 26,899 70,519 80,697 211,557 2,609,203 7,827,609

Collatz Trajectory (173 steps to reach 1)

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

7,827,609 23,482,828 11,741,414 5,870,707 17,612,122 8,806,061 26,418,184 13,209,092 6,604,546 3,302,273 9,906,820 4,953,410 2,476,705 7,430,116 3,715,058 1,857,529 5,572,588 2,786,294 1,393,147 4,179,442 2,089,721 6,269,164 3,134,582 1,567,291 4,701,874 2,350,937 7,052,812 3,526,406 1,763,203 5,289,610 2,644,805 7,934,416 3,967,208 1,983,604 991,802 495,901 1,487,704 743,852 371,926 185,963 557,890 278,945 836,836 418,418 209,209 627,628 313,814 156,907 470,722 235,361 706,084 353,042 176,521 529,564 264,782 132,391 397,174 198,587 595,762 297,881

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