8,640,464

2⁴ × 7² × 103 × 107

Starting at 8,640,464, the Collatz iteration reaches 1 after 67 steps. The first transition is 4320232; the starting value is even with 60 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 7^2 × 103 × 107

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 60

Divisor Sum (σ) 19,846,944

Proper Divisor Sum 11,206,480

Digit Sum / Digital Root 32 (Root: 5)

Adjacent Primes #8640451 ← → #8640481

Radix Representation

Decimal	8640464
Binary	100000111101011111010000 (24 bits)
Octal	0o40753720
Hexadecimal	0x83D7D0

Divisor Catalog (60)

1 2 4 7 8 14 16 28 49 56 98 103 107 112 196 206 214 392 412 428 721 749 784 824 856 1,442 1,498 1,648 1,712 2,884 2,996 5,047 5,243 5,768 5,992 10,094 10,486 11,021 11,536 11,984 20,188 20,972 22,042 40,376 41,944 44,084 77,147 80,752 83,888 88,168 154,294 176,336 308,588 540,029 617,176 1,080,058 1,234,352 2,160,116 4,320,232 8,640,464

Collatz Trajectory (67 steps to reach 1)

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

8,640,464 4,320,232 2,160,116 1,080,058 540,029 1,620,088 810,044 405,022 202,511 607,534 303,767 911,302 455,651 1,366,954 683,477 2,050,432 1,025,216 512,608 256,304 128,152 64,076 32,038 16,019 48,058 24,029 72,088 36,044 18,022 9,011 27,034 13,517 40,552 20,276 10,138 5,069 15,208 7,604 3,802 1,901 5,704 2,852 1,426 713 2,140 1,070 535 1,606 803 2,410 1,205 3,616 1,808 904 452 226 113 340 170 85 256

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