10,746,736

2⁴ × 7 × 11² × 13 × 61

10,746,736 factors as 2^4 × 7 × 11^2 × 13 × 61. Its 120 positive divisors give a proper-divisor sum of 17,883,376, so this integer is abundant. The Collatz stopping time is 202 steps.

Prime Factor Structure

Factorization String 2^4 × 7 × 11^2 × 13 × 61

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 120

Divisor Sum (σ) 28,630,112

Proper Divisor Sum 17,883,376

Digit Sum / Digital Root 34 (Root: 7)

Adjacent Primes #10746731 ← → #10746763

Radix Representation

Decimal	10746736
Binary	101000111111101101110000 (24 bits)
Octal	0o50775560
Hexadecimal	0xA3FB70

Divisor Catalog (60 of 120)

1 2 4 7 8 11 13 14 16 22 26 28 44 52 56 61 77 88 91 104 112 121 122 143 154 176 182 208 242 244 286 308 364 427 484 488 572 616 671 728 793 847 854 968 976 1,001 1,144 1,232 1,342 1,456 1,573 1,586 1,694 1,708 1,936 2,002 2,288 2,684 3,146 3,172

Collatz Trajectory (202 steps to reach 1)

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

10,746,736 5,373,368 2,686,684 1,343,342 671,671 2,015,014 1,007,507 3,022,522 1,511,261 4,533,784 2,266,892 1,133,446 566,723 1,700,170 850,085 2,550,256 1,275,128 637,564 318,782 159,391 478,174 239,087 717,262 358,631 1,075,894 537,947 1,613,842 806,921 2,420,764 1,210,382 605,191 1,815,574 907,787 2,723,362 1,361,681 4,085,044 2,042,522 1,021,261 3,063,784 1,531,892 765,946 382,973 1,148,920 574,460 287,230 143,615 430,846 215,423 646,270 323,135 969,406 484,703 1,454,110 727,055 2,181,166 1,090,583 3,271,750 1,635,875 4,907,626 2,453,813

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