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Atlas › Integer Profiles › Node 10,227,100

10,227,100

22 × 52 × 13 × 7867
Abundant Even Composite

10,227,100 factors as 2^2 × 5^2 × 13 × 7867. Its 36 positive divisors give a proper-divisor sum of 13,675,884, so this integer is abundant. The Collatz stopping time is 132 steps.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 13 × 7867
Distinct Prime Factors 4
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 36
Divisor Sum (σ) 23,902,984
Proper Divisor Sum 13,675,884
Digit Sum / Digital Root 13 (Root: 4)
Adjacent Primes #10227097 ← → #10227121

Radix Representation

Decimal 10227100
Binary 100111000000110110011100 (24 bits)
Octal 0o47006634
Hexadecimal 0x9C0D9C

Divisor Catalog (36)

1 2 4 5 10 13 20 25 26 50 52 65 100 130 260 325 650 1,300 7,867 15,734 31,468 39,335 78,670 102,271 157,340 196,675 204,542 393,350 409,084 511,355 786,700 1,022,710 2,045,420 2,556,775 5,113,550 10,227,100

Collatz Trajectory (132 steps to reach 1)

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

10,227,100 5,113,550 2,556,775 7,670,326 3,835,163 11,505,490 5,752,745 17,258,236 8,629,118 4,314,559 12,943,678 6,471,839 19,415,518 9,707,759 29,123,278 14,561,639 43,684,918 21,842,459 65,527,378 32,763,689 98,291,068 49,145,534 24,572,767 73,718,302 36,859,151 110,577,454 55,288,727 165,866,182 82,933,091 248,799,274 124,399,637 373,198,912 186,599,456 93,299,728 46,649,864 23,324,932 11,662,466 5,831,233 17,493,700 8,746,850 4,373,425 13,120,276 6,560,138 3,280,069 9,840,208 4,920,104 2,460,052 1,230,026 615,013 1,845,040 922,520 461,260 230,630 115,315 345,946 172,973 518,920 259,460 129,730 64,865

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