620,340

2² × 3 × 5 × 7² × 211

Starting at 620,340, the Collatz iteration reaches 1 after 79 steps. The first transition is 310170; the starting value is even with 72 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 7^2 × 211

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,030,112

Proper Divisor Sum 1,409,772

Digit Sum / Digital Root 15 (Root: 6)

Adjacent Primes #620329 ← → #620351

Radix Representation

Decimal	620340
Binary	10010111011100110100 (20 bits)
Octal	0o2273464
Hexadecimal	0x97734

Divisor Catalog (60 of 72)

1 2 3 4 5 6 7 10 12 14 15 20 21 28 30 35 42 49 60 70 84 98 105 140 147 196 210 211 245 294 420 422 490 588 633 735 844 980 1,055 1,266 1,470 1,477 2,110 2,532 2,940 2,954 3,165 4,220 4,431 5,908 6,330 7,385 8,862 10,339 12,660 14,770 17,724 20,678 22,155 29,540

Collatz Trajectory (79 steps to reach 1)

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

620,340 310,170 155,085 465,256 232,628 116,314 58,157 174,472 87,236 43,618 21,809 65,428 32,714 16,357 49,072 24,536 12,268 6,134 3,067 9,202 4,601 13,804 6,902 3,451 10,354 5,177 15,532 7,766 3,883 11,650 5,825 17,476 8,738 4,369 13,108 6,554 3,277 9,832 4,916 2,458 1,229 3,688 1,844 922 461 1,384 692 346 173 520 260 130 65 196 98 49 148 74 37 112

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