Question

which of the following shows the prime factorization of 220?
a) $10 \cdot 2 \cdot 11$
b) $22 \cdot 10$
c) $2 \cdot 3^2 \cdot 5$
d) $2^2 \cdot 5 \cdot 11$

Explanation:

Step1: Divide 220 by smallest prime

$220 \div 2 = 110$

Step2: Divide result by 2 again

$110 \div 2 = 55$

Step3: Divide result by next prime 5

$55 \div 5 = 11$

Step4: 11 is prime, stop. Count prime factors

We have two 2s, one 5, one 11: $2^2 \cdot 5 \cdot 11$

Step5: Eliminate invalid options

• a) 10 is not prime; b) 22,10 not prime; c) 3 is not a factor of 220

Answer:

d) $2^2 \cdot 5 \cdot 11$