7,742,664

2³ × 3² × 53 × 2029

7,742,664 has the prime decomposition 2^3 × 3^2 × 53 × 2029. Its 4 distinct prime factors produce 48 positive divisors.

Prime Factor Structure

Factorization String 2^3 × 3^2 × 53 × 2029

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 21,375,900

Proper Divisor Sum 13,633,236

Digit Sum / Digital Root 36 (Root: 9)

Adjacent Primes #7742641 ← → #7742677

Radix Representation

Decimal	7742664
Binary	11101100010010011001000 (23 bits)
Octal	0o35422310
Hexadecimal	0x7624C8

Divisor Catalog (48)

1 2 3 4 6 8 9 12 18 24 36 53 72 106 159 212 318 424 477 636 954 1,272 1,908 2,029 3,816 4,058 6,087 8,116 12,174 16,232 18,261 24,348 36,522 48,696 73,044 107,537 146,088 215,074 322,611 430,148 645,222 860,296 967,833 1,290,444 1,935,666 2,580,888 3,871,332 7,742,664

Collatz Trajectory (98 steps to reach 1)

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

7,742,664 3,871,332 1,935,666 967,833 2,903,500 1,451,750 725,875 2,177,626 1,088,813 3,266,440 1,633,220 816,610 408,305 1,224,916 612,458 306,229 918,688 459,344 229,672 114,836 57,418 28,709 86,128 43,064 21,532 10,766 5,383 16,150 8,075 24,226 12,113 36,340 18,170 9,085 27,256 13,628 6,814 3,407 10,222 5,111 15,334 7,667 23,002 11,501 34,504 17,252 8,626 4,313 12,940 6,470 3,235 9,706 4,853 14,560 7,280 3,640 1,820 910 455 1,366

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