Question

which of the following shows the prime factorization of 132?
a) $2^3 \cdot 3 \cdot 11$
b) $2^2 \cdot 3^2 \cdot 7$
c) $2^2 \cdot 3 \cdot 11$
d) $2^3 \cdot 3^2 \cdot 5$

Explanation:

Step1: Divide 132 by smallest prime

$132 \div 2 = 66$

Step2: Divide quotient by 2 again

$66 \div 2 = 33$

Step3: Divide quotient by next prime

$33 \div 3 = 11$

Step4: 11 is prime, stop.

Prime factors: $2^2 \cdot 3 \cdot 11$

Step5: Match with options

Compare to given choices.

Answer:

c) $2^{2} \cdot 3 \cdot 11$