7,877,705

5 × 11² × 29 × 449

Starting at 7,877,705, the Collatz iteration reaches 1 after 261 steps. The first transition is 23633116; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 5 × 11^2 × 29 × 449

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 10,773,000

Proper Divisor Sum 2,895,295

Digit Sum / Digital Root 41 (Root: 5)

Adjacent Primes #7877693 ← → #7877711

Radix Representation

Decimal	7877705
Binary	11110000011010001001001 (23 bits)
Octal	0o36032111
Hexadecimal	0x783449

Divisor Catalog (24)

1 5 11 29 55 121 145 319 449 605 1,595 2,245 3,509 4,939 13,021 17,545 24,695 54,329 65,105 143,231 271,645 716,155 1,575,541 7,877,705

Collatz Trajectory (261 steps to reach 1)

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

7,877,705 23,633,116 11,816,558 5,908,279 17,724,838 8,862,419 26,587,258 13,293,629 39,880,888 19,940,444 9,970,222 4,985,111 14,955,334 7,477,667 22,433,002 11,216,501 33,649,504 16,824,752 8,412,376 4,206,188 2,103,094 1,051,547 3,154,642 1,577,321 4,731,964 2,365,982 1,182,991 3,548,974 1,774,487 5,323,462 2,661,731 7,985,194 3,992,597 11,977,792 5,988,896 2,994,448 1,497,224 748,612 374,306 187,153 561,460 280,730 140,365 421,096 210,548 105,274 52,637 157,912 78,956 39,478 19,739 59,218 29,609 88,828 44,414 22,207 66,622 33,311 99,934 49,967

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