λ
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Atlas › Integer Profiles › Node 9,727,600

9,727,600

24 × 52 × 83 × 293
Abundant Even Composite

9,727,600 factors as 2^4 × 5^2 × 83 × 293. Its 60 positive divisors give a proper-divisor sum of 14,005,256, so this integer is abundant. The Collatz stopping time is 194 steps.

Prime Factor Structure

Factorization String 2^4 × 5^2 × 83 × 293
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 60
Divisor Sum (σ) 23,732,856
Proper Divisor Sum 14,005,256
Digit Sum / Digital Root 31 (Root: 4)
Adjacent Primes #9727579 ← → #9727603

Radix Representation

Decimal 9727600
Binary 100101000110111001110000 (24 bits)
Octal 0o45067160
Hexadecimal 0x946E70

Divisor Catalog (60)

1 2 4 5 8 10 16 20 25 40 50 80 83 100 166 200 293 332 400 415 586 664 830 1,172 1,328 1,465 1,660 2,075 2,344 2,930 3,320 4,150 4,688 5,860 6,640 7,325 8,300 11,720 14,650 16,600 23,440 24,319 29,300 33,200 48,638 58,600 97,276 117,200 121,595 194,552 243,190 389,104 486,380 607,975 972,760 1,215,950 1,945,520 2,431,900 4,863,800 9,727,600

Collatz Trajectory (194 steps to reach 1)

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

9,727,600 4,863,800 2,431,900 1,215,950 607,975 1,823,926 911,963 2,735,890 1,367,945 4,103,836 2,051,918 1,025,959 3,077,878 1,538,939 4,616,818 2,308,409 6,925,228 3,462,614 1,731,307 5,193,922 2,596,961 7,790,884 3,895,442 1,947,721 5,843,164 2,921,582 1,460,791 4,382,374 2,191,187 6,573,562 3,286,781 9,860,344 4,930,172 2,465,086 1,232,543 3,697,630 1,848,815 5,546,446 2,773,223 8,319,670 4,159,835 12,479,506 6,239,753 18,719,260 9,359,630 4,679,815 14,039,446 7,019,723 21,059,170 10,529,585 31,588,756 15,794,378 7,897,189 23,691,568 11,845,784 5,922,892 2,961,446 1,480,723 4,442,170 2,221,085

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