147,784

2³ × 7² × 13 × 29

147,784 factors as 2^3 × 7^2 × 13 × 29. Its 48 positive divisors give a proper-divisor sum of 211,316, so this integer is abundant. The Collatz stopping time is 95 steps.

Prime Factor Structure

Factorization String 2^3 × 7^2 × 13 × 29

Distinct Prime Factors 4

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 48

Divisor Sum (σ) 359,100

Proper Divisor Sum 211,316

Digit Sum / Digital Root 31 (Root: 4)

Adjacent Primes #147779 ← → #147787

Radix Representation

Decimal	147784
Binary	100100000101001000 (18 bits)
Octal	0o440510
Hexadecimal	0x24148

Divisor Catalog (48)

1 2 4 7 8 13 14 26 28 29 49 52 56 58 91 98 104 116 182 196 203 232 364 377 392 406 637 728 754 812 1,274 1,421 1,508 1,624 2,548 2,639 2,842 3,016 5,096 5,278 5,684 10,556 11,368 18,473 21,112 36,946 73,892 147,784

Collatz Trajectory (95 steps to reach 1)

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

147,784 73,892 36,946 18,473 55,420 27,710 13,855 41,566 20,783 62,350 31,175 93,526 46,763 140,290 70,145 210,436 105,218 52,609 157,828 78,914 39,457 118,372 59,186 29,593 88,780 44,390 22,195 66,586 33,293 99,880 49,940 24,970 12,485 37,456 18,728 9,364 4,682 2,341 7,024 3,512 1,756 878 439 1,318 659 1,978 989 2,968 1,484 742 371 1,114 557 1,672 836 418 209 628 314 157

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