6,825,700

2² × 5² × 7³ × 199

Starting at 6,825,700, the Collatz iteration reaches 1 after 77 steps. The first transition is 3412850; the starting value is even with 72 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 5^2 × 7^3 × 199

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 17,360,000

Proper Divisor Sum 10,534,300

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #6825697 ← → #6825703

Radix Representation

Decimal	6825700
Binary	11010000010011011100100 (23 bits)
Octal	0o32023344
Hexadecimal	0x6826E4

Divisor Catalog (60 of 72)

1 2 4 5 7 10 14 20 25 28 35 49 50 70 98 100 140 175 196 199 245 343 350 398 490 686 700 796 980 995 1,225 1,372 1,393 1,715 1,990 2,450 2,786 3,430 3,980 4,900 4,975 5,572 6,860 6,965 8,575 9,751 9,950 13,930 17,150 19,502 19,900 27,860 34,300 34,825 39,004 48,755 68,257 69,650 97,510 136,514

Collatz Trajectory (77 steps to reach 1)

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

6,825,700 3,412,850 1,706,425 5,119,276 2,559,638 1,279,819 3,839,458 1,919,729 5,759,188 2,879,594 1,439,797 4,319,392 2,159,696 1,079,848 539,924 269,962 134,981 404,944 202,472 101,236 50,618 25,309 75,928 37,964 18,982 9,491 28,474 14,237 42,712 21,356 10,678 5,339 16,018 8,009 24,028 12,014 6,007 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

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