31,564

2² × 13 × 607

Starting at 31,564, the Collatz iteration reaches 1 after 103 steps. The first transition is 15782; the starting value is even with 12 positive divisors.

Prime Factor Structure

Factorization String 2^2 × 13 × 607

Distinct Prime Factors 3

Square Status No

Abundance Measure Deficient

Analytical Properties

Total Divisors 12

Divisor Sum (σ) 59,584

Proper Divisor Sum 28,020

Digit Sum / Digital Root 19 (Root: 1)

Adjacent Primes #31547 ← → #31567

Radix Representation

Decimal	31564
Binary	111101101001100 (15 bits)
Octal	0o75514
Hexadecimal	0x7B4C

Divisor Catalog (12)

1 2 4 13 26 52 607 1,214 2,428 7,891 15,782 31,564

Collatz Trajectory (103 steps to reach 1)

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

31,564 15,782 7,891 23,674 11,837 35,512 17,756 8,878 4,439 13,318 6,659 19,978 9,989 29,968 14,984 7,492 3,746 1,873 5,620 2,810 1,405 4,216 2,108 1,054 527 1,582 791 2,374 1,187 3,562 1,781 5,344 2,672 1,336 668 334 167 502 251 754 377 1,132 566 283 850 425 1,276 638 319 958 479 1,438 719 2,158 1,079 3,238 1,619 4,858 2,429 7,288

← Previous Integer #31,563 Browse Full Index Next Integer #31,565 →