λ
Ratio Atlas
Atlas › Integer Profiles › Node 9,991,000

9,991,000

23 × 53 × 97 × 103
Abundant Even Composite

9,991,000 factors as 2^3 × 5^3 × 97 × 103. Its 64 positive divisors give a proper-divisor sum of 13,858,280, so this integer is abundant. The Collatz stopping time is 163 steps.

Prime Factor Structure

Factorization String 2^3 × 5^3 × 97 × 103
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 64
Divisor Sum (σ) 23,849,280
Proper Divisor Sum 13,858,280
Digit Sum / Digital Root 28 (Root: 1)
Adjacent Primes #9990997 ← → #9991027

Radix Representation

Decimal 9991000
Binary 100110000111001101011000 (24 bits)
Octal 0o46071530
Hexadecimal 0x987358

Divisor Catalog (60 of 64)

1 2 4 5 8 10 20 25 40 50 97 100 103 125 194 200 206 250 388 412 485 500 515 776 824 970 1,000 1,030 1,940 2,060 2,425 2,575 3,880 4,120 4,850 5,150 9,700 9,991 10,300 12,125 12,875 19,400 19,982 20,600 24,250 25,750 39,964 48,500 49,955 51,500 79,928 97,000 99,910 103,000 199,820 249,775 399,640 499,550 999,100 1,248,875

Collatz Trajectory (163 steps to reach 1)

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

9,991,000 4,995,500 2,497,750 1,248,875 3,746,626 1,873,313 5,619,940 2,809,970 1,404,985 4,214,956 2,107,478 1,053,739 3,161,218 1,580,609 4,741,828 2,370,914 1,185,457 3,556,372 1,778,186 889,093 2,667,280 1,333,640 666,820 333,410 166,705 500,116 250,058 125,029 375,088 187,544 93,772 46,886 23,443 70,330 35,165 105,496 52,748 26,374 13,187 39,562 19,781 59,344 29,672 14,836 7,418 3,709 11,128 5,564 2,782 1,391 4,174 2,087 6,262 3,131 9,394 4,697 14,092 7,046 3,523 10,570

More profiles

Browse other published profiles and their separate link collections.

Profile #8,342,168 Profile #1,146,956 Profile #9,712,347 Profile #6,573,969 Profile #965,653 Profile #4,620,983 Profile #853,259 Profile #1,288,150
← Previous Integer #9,990,999 Browse Full Index Next Integer #9,991,001 →