λ
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Atlas › Integer Profiles › Node 10,706,150

10,706,150

2 × 52 × 7 × 132 × 181
Abundant Even Composite

10,706,150 factors as 2 × 5^2 × 7 × 13^2 × 181. Its 72 positive divisors give a proper-divisor sum of 14,073,514, so this integer is abundant. The Collatz stopping time is 171 steps.

Prime Factor Structure

Factorization String 2 × 5^2 × 7 × 13^2 × 181
Distinct Prime Factors 5
Square Status No
Abundance Measure Abundant

Analytical Properties

Total Divisors 72
Divisor Sum (σ) 24,779,664
Proper Divisor Sum 14,073,514
Digit Sum / Digital Root 20 (Root: 2)
Adjacent Primes #10706119 ← → #10706167

Radix Representation

Decimal 10706150
Binary 101000110101110011100110 (24 bits)
Octal 0o50656346
Hexadecimal 0xA35CE6

Divisor Catalog (60 of 72)

1 2 5 7 10 13 14 25 26 35 50 65 70 91 130 169 175 181 182 325 338 350 362 455 650 845 905 910 1,183 1,267 1,690 1,810 2,275 2,353 2,366 2,534 4,225 4,525 4,550 4,706 5,915 6,335 8,450 9,050 11,765 11,830 12,670 16,471 23,530 29,575 30,589 31,675 32,942 58,825 59,150 61,178 63,350 82,355 117,650 152,945

Collatz Trajectory (171 steps to reach 1)

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

10,706,150 5,353,075 16,059,226 8,029,613 24,088,840 12,044,420 6,022,210 3,011,105 9,033,316 4,516,658 2,258,329 6,774,988 3,387,494 1,693,747 5,081,242 2,540,621 7,621,864 3,810,932 1,905,466 952,733 2,858,200 1,429,100 714,550 357,275 1,071,826 535,913 1,607,740 803,870 401,935 1,205,806 602,903 1,808,710 904,355 2,713,066 1,356,533 4,069,600 2,034,800 1,017,400 508,700 254,350 127,175 381,526 190,763 572,290 286,145 858,436 429,218 214,609 643,828 321,914 160,957 482,872 241,436 120,718 60,359 181,078 90,539 271,618 135,809 407,428

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