Step 1 of 4 · Why k+1 factors?
Let's start small. What are all the factors of 8?
8 = 2 × 2 × 2
A factor of 8 can only be built from 2's — so the only choice is how many to use.
all factors of 8
1, 2, 4, 8
4 choices (0, 1, 2, or 3 twos) → 4 factors
The pattern: if N = pk, you can use 0, 1, 2, ..., k copies of p.
That's k + 1 choices → k + 1 factors.
Step 2 of 4 · Factor 32 = 2⁵
32
Climb the powers of 2 from 2⁰ up to 2⁵.
all factors of 32
1, 2, 4, 8, 16, 32 (6 factors)
Step 3 of 4 · Factor 81 = 3⁴
81
Same idea — climb powers of 3.
all factors of 81
1, 3, 9, 27, 81 (5 factors)
Step 4 of 4 · Your turn
Pick the full list of factors.
🏆
Nice work!
You climbed all the staircases.