507,920

2⁴ × 5 × 7 × 907

507,920 factors as 2^4 × 5 × 7 × 907. Its 40 positive divisors give a proper-divisor sum of 843,184, so this integer is abundant. The Collatz stopping time is 107 steps.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 907

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 40

Divisor Sum (σ) 1,351,104

Proper Divisor Sum 843,184

Digit Sum / Digital Root 23 (Root: 5)

Adjacent Primes #507919 ← → #507937

Radix Representation

Decimal	507920
Binary	1111100000000010000 (19 bits)
Octal	0o1740020
Hexadecimal	0x7C010

Divisor Catalog (40)

1 2 4 5 7 8 10 14 16 20 28 35 40 56 70 80 112 140 280 560 907 1,814 3,628 4,535 6,349 7,256 9,070 12,698 14,512 18,140 25,396 31,745 36,280 50,792 63,490 72,560 101,584 126,980 253,960 507,920

Collatz Trajectory (107 steps to reach 1)

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

507,920 253,960 126,980 63,490 31,745 95,236 47,618 23,809 71,428 35,714 17,857 53,572 26,786 13,393 40,180 20,090 10,045 30,136 15,068 7,534 3,767 11,302 5,651 16,954 8,477 25,432 12,716 6,358 3,179 9,538 4,769 14,308 7,154 3,577 10,732 5,366 2,683 8,050 4,025 12,076 6,038 3,019 9,058 4,529 13,588 6,794 3,397 10,192 5,096 2,548 1,274 637 1,912 956 478 239 718 359 1,078 539

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