Question

which of the following shows the prime factorization of 90?
a) $3^2 \cdot 10$
b) $2 \cdot 9 \cdot 5$
c) $2 \cdot 3^2 \cdot 5$
d) $2^3 \cdot 3 \cdot 5$

Explanation:

Step1: Factor 90 into small primes

$90 = 2 \times 45$

Step2: Factor 45 further

$45 = 3 \times 15$

Step3: Factor 15 completely

$15 = 3 \times 5$

Step4: Combine and simplify exponents

$90 = 2 \times 3 \times 3 \times 5 = 2 \cdot 3^2 \cdot 5$

Step5: Match with options

Compare to given choices.

Answer:

c) $2 \cdot 3^2 \cdot 5$