7,727,824

2⁴ × 13 × 53 × 701

7,727,824 has the prime decomposition 2^4 × 13 × 53 × 701. Its 4 distinct prime factors produce 40 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 13 × 53 × 701

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 16,452,072

Proper Divisor Sum 8,724,248

Digit Sum / Digital Root 37 (Root: 1)

Adjacent Primes #7727807 ← → #7727827

Radix Representation

Decimal	7727824
Binary	11101011110101011010000 (23 bits)
Octal	0o35365320
Hexadecimal	0x75EAD0

Divisor Catalog (40)

1 2 4 8 13 16 26 52 53 104 106 208 212 424 689 701 848 1,378 1,402 2,756 2,804 5,512 5,608 9,113 11,024 11,216 18,226 36,452 37,153 72,904 74,306 145,808 148,612 297,224 482,989 594,448 965,978 1,931,956 3,863,912 7,727,824

Collatz Trajectory (98 steps to reach 1)

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

7,727,824 3,863,912 1,931,956 965,978 482,989 1,448,968 724,484 362,242 181,121 543,364 271,682 135,841 407,524 203,762 101,881 305,644 152,822 76,411 229,234 114,617 343,852 171,926 85,963 257,890 128,945 386,836 193,418 96,709 290,128 145,064 72,532 36,266 18,133 54,400 27,200 13,600 6,800 3,400 1,700 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288 3,644 1,822 911 2,734 1,367

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