782,748

2² × 3² × 17 × 1279

782,748 factors as 2^2 × 3^2 × 17 × 1279. Its 36 positive divisors give a proper-divisor sum of 1,313,892, so this integer is abundant. The Collatz stopping time is 224 steps.

Prime Factor Structure

Factorization String 2^2 × 3^2 × 17 × 1279

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 36

Divisor Sum (σ) 2,096,640

Proper Divisor Sum 1,313,892

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #782723 ← → #782777

Radix Representation

Decimal	782748
Binary	10111111000110011100 (20 bits)
Octal	0o2770634
Hexadecimal	0xBF19C

Divisor Catalog (36)

1 2 3 4 6 9 12 17 18 34 36 51 68 102 153 204 306 612 1,279 2,558 3,837 5,116 7,674 11,511 15,348 21,743 23,022 43,486 46,044 65,229 86,972 130,458 195,687 260,916 391,374 782,748

Collatz Trajectory (224 steps to reach 1)

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

782,748 391,374 195,687 587,062 293,531 880,594 440,297 1,320,892 660,446 330,223 990,670 495,335 1,486,006 743,003 2,229,010 1,114,505 3,343,516 1,671,758 835,879 2,507,638 1,253,819 3,761,458 1,880,729 5,642,188 2,821,094 1,410,547 4,231,642 2,115,821 6,347,464 3,173,732 1,586,866 793,433 2,380,300 1,190,150 595,075 1,785,226 892,613 2,677,840 1,338,920 669,460 334,730 167,365 502,096 251,048 125,524 62,762 31,381 94,144 47,072 23,536 11,768 5,884 2,942 1,471 4,414 2,207 6,622 3,311 9,934 4,967

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