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Atlas › Integer Profiles › Node 9,720,072

9,720,072

23 × 32 × 127 × 1063
Abundant Even Composite

9,720,072 factors as 2^3 × 3^2 × 127 × 1063. Its 48 positive divisors give a proper-divisor sum of 16,837,368, so this integer is abundant. The Collatz stopping time is 62 steps.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 127 × 1063
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 48
Divisor Sum (σ) 26,557,440
Proper Divisor Sum 16,837,368
Digit Sum / Digital Root 27 (Root: 9)
Adjacent Primes #9720043 ← → #9720083

Radix Representation

Decimal 9720072
Binary 100101000101000100001000 (24 bits)
Octal 0o45050410
Hexadecimal 0x945108

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 72 127 254 381 508 762 1,016 1,063 1,143 1,524 2,126 2,286 3,048 3,189 4,252 4,572 6,378 8,504 9,144 9,567 12,756 19,134 25,512 38,268 76,536 135,001 270,002 405,003 540,004 810,006 1,080,008 1,215,009 1,620,012 2,430,018 3,240,024 4,860,036 9,720,072

Collatz Trajectory (62 steps to reach 1)

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

9,720,072 4,860,036 2,430,018 1,215,009 3,645,028 1,822,514 911,257 2,733,772 1,366,886 683,443 2,050,330 1,025,165 3,075,496 1,537,748 768,874 384,437 1,153,312 576,656 288,328 144,164 72,082 36,041 108,124 54,062 27,031 81,094 40,547 121,642 60,821 182,464 91,232 45,616 22,808 11,404 5,702 2,851 8,554 4,277 12,832 6,416 3,208 1,604 802 401 1,204 602 301 904 452 226 113 340 170 85 256 128 64 32 16 8

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