3,692,640

2⁵ × 3 × 5 × 7² × 157

3,692,640 has the prime decomposition 2^5 × 3 × 5 × 7^2 × 157. Its 5 distinct prime factors produce 144 positive divisors.

Prime Factor Structure

Factorization String 2^5 × 3 × 5 × 7^2 × 157

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 144

Divisor Sum (σ) 13,617,072

Proper Divisor Sum 9,924,432

Digit Sum / Digital Root 30 (Root: 3)

Adjacent Primes #3692617 ← → #3692641

Radix Representation

Decimal	3692640
Binary	1110000101100001100000 (22 bits)
Octal	0o16054140
Hexadecimal	0x385860

Divisor Catalog (60 of 144)

1 2 3 4 5 6 7 8 10 12 14 15 16 20 21 24 28 30 32 35 40 42 48 49 56 60 70 80 84 96 98 105 112 120 140 147 157 160 168 196 210 224 240 245 280 294 314 336 392 420 471 480 490 560 588 628 672 735 784 785

Collatz Trajectory (172 steps to reach 1)

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

3,692,640 1,846,320 923,160 461,580 230,790 115,395 346,186 173,093 519,280 259,640 129,820 64,910 32,455 97,366 48,683 146,050 73,025 219,076 109,538 54,769 164,308 82,154 41,077 123,232 61,616 30,808 15,404 7,702 3,851 11,554 5,777 17,332 8,666 4,333 13,000 6,500 3,250 1,625 4,876 2,438 1,219 3,658 1,829 5,488 2,744 1,372 686 343 1,030 515 1,546 773 2,320 1,160 580 290 145 436 218 109

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