6,427,827

3² × 7 × 257 × 397

Starting at 6,427,827, the Collatz iteration reaches 1 after 121 steps. The first transition is 19283482; the starting value is odd with 24 positive divisors.

Prime Factor Structure

Factorization String 3^2 × 7 × 257 × 397

Distinct Prime Factors 4

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 24

Divisor Sum (σ) 10,679,136

Proper Divisor Sum 4,251,309

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #6427807 ← → #6427831

Radix Representation

Decimal	6427827
Binary	11000100001010010110011 (23 bits)
Octal	0o30412263
Hexadecimal	0x6214B3

Divisor Catalog (24)

Collatz Trajectory (121 steps to reach 1)

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

6,427,827 19,283,482 9,641,741 28,925,224 14,462,612 7,231,306 3,615,653 10,846,960 5,423,480 2,711,740 1,355,870 677,935 2,033,806 1,016,903 3,050,710 1,525,355 4,576,066 2,288,033 6,864,100 3,432,050 1,716,025 5,148,076 2,574,038 1,287,019 3,861,058 1,930,529 5,791,588 2,895,794 1,447,897 4,343,692 2,171,846 1,085,923 3,257,770 1,628,885 4,886,656 2,443,328 1,221,664 610,832 305,416 152,708 76,354 38,177 114,532 57,266 28,633 85,900 42,950 21,475 64,426 32,213 96,640 48,320 24,160 12,080 6,040 3,020 1,510 755 2,266 1,133

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