3,406,410

2 × 3² × 5 × 7 × 5407

Starting at 3,406,410, the Collatz iteration reaches 1 after 84 steps. The first transition is 1703205; the starting value is even with 48 positive divisors.

Prime Factor Structure

Factorization String 2 × 3^2 × 5 × 7 × 5407

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 10,123,776

Proper Divisor Sum 6,717,366

Digit Sum / Digital Root 18 (Root: 9)

Adjacent Primes #3406391 ← → #3406421

Radix Representation

Decimal	3406410
Binary	1100111111101001001010 (22 bits)
Octal	0o14775112
Hexadecimal	0x33FA4A

Divisor Catalog (48)

1 2 3 5 6 7 9 10 14 15 18 21 30 35 42 45 63 70 90 105 126 210 315 630 5,407 10,814 16,221 27,035 32,442 37,849 48,663 54,070 75,698 81,105 97,326 113,547 162,210 189,245 227,094 243,315 340,641 378,490 486,630 567,735 681,282 1,135,470 1,703,205 3,406,410

Collatz Trajectory (84 steps to reach 1)

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

3,406,410 1,703,205 5,109,616 2,554,808 1,277,404 638,702 319,351 958,054 479,027 1,437,082 718,541 2,155,624 1,077,812 538,906 269,453 808,360 404,180 202,090 101,045 303,136 151,568 75,784 37,892 18,946 9,473 28,420 14,210 7,105 21,316 10,658 5,329 15,988 7,994 3,997 11,992 5,996 2,998 1,499 4,498 2,249 6,748 3,374 1,687 5,062 2,531 7,594 3,797 11,392 5,696 2,848 1,424 712 356 178 89 268 134 67 202 101

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