7,448,400

2⁴ × 3² × 5² × 2069

Starting at 7,448,400, the Collatz iteration reaches 1 after 67 steps. The first transition is 3724200; the starting value is even with 90 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 3^2 × 5^2 × 2069

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 90

Divisor Sum (σ) 25,860,510

Proper Divisor Sum 18,412,110

Digit Sum / Digital Root 27 (Root: 9)

Adjacent Primes #7448387 ← → #7448407

Radix Representation

Decimal	7448400
Binary	11100011010011101010000 (23 bits)
Octal	0o34323520
Hexadecimal	0x71A750

Divisor Catalog (60 of 90)

1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36 40 45 48 50 60 72 75 80 90 100 120 144 150 180 200 225 240 300 360 400 450 600 720 900 1,200 1,800 2,069 3,600 4,138 6,207 8,276 10,345 12,414 16,552 18,621 20,690 24,828 31,035 33,104 37,242 41,380 49,656

Collatz Trajectory (67 steps to reach 1)

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

7,448,400 3,724,200 1,862,100 931,050 465,525 1,396,576 698,288 349,144 174,572 87,286 43,643 130,930 65,465 196,396 98,198 49,099 147,298 73,649 220,948 110,474 55,237 165,712 82,856 41,428 20,714 10,357 31,072 15,536 7,768 3,884 1,942 971 2,914 1,457 4,372 2,186 1,093 3,280 1,640 820 410 205 616 308 154 77 232 116 58 29 88 44 22 11 34 17 52 26 13 40

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