Step 1 of 4 · Peel the sign
−12 = ?
A negative number is always (−1) × (its positive twin). So pull off the sign first, then prime factorize what's left.
12 = 2 × 2 × 3
So −12 = (−1) × 2 × 2 × 3 = −1 × 2² × 3
Step 2 of 4 · Factor tree for −36
Prime factorize −36
Start by peeling −1, then factor 36 the usual way.
−36 = (−1) × 2² × 3² = −2² × 3²
Step 3 of 4 · Check it
Does −1 × 2 × 2 × 3 × 3 = −36 ?
Multiply the prime factors back together. The (−1) is what makes the answer negative.
2 × 2 = 4
4 × 3 = 12
12 × 3 = 36
(−1) × 36 = −36 ✓
prime factors stay the same — only the (−1) changes
Step 4 of 4 · Your turn
Prime factorize −24
First peel the −1. Then pick primes that divide the quotient.
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Nice work!
You factorized them all.