Question

which of the following shows the prime factorization of 220? a) 10·2·11 b) 22·10 c) 2·3²·5 d) 2²·5·11

Explanation:

Step1: Divide by smallest prime (2)

$220 \div 2 = 110$

Step2: Divide result by 2 again

$110 \div 2 = 55$

Step3: Divide by next prime (5)

$55 \div 5 = 11$

Step4: 11 is prime, stop. Count primes

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

Step5: Verify other options

a) $10 \cdot 2 \cdot 11$: 10 is not prime.
b) $22 \cdot 10$: 22 and 10 are not prime.
c) $2 \cdot 3^2 \cdot 5$: $2 \cdot 9 \cdot 5 = 90
eq 220$.

Answer:

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