Write the prime factors of 72 in index notation.A23×32B23×33C24×33D21×32E23×3×11
Question
Write the prime factors of 72 in index notation.
A) 2<sup>3</sup> × 3<sup>2</sup>
B) 2<sup>3</sup> × 3<sup>3</sup>
C) 2<sup>4</sup> × 3<sup>3</sup>
D) 2<sup>1</sup> × 3<sup>2</sup>
E) 2<sup>3</sup> × 3 × 1<sup>1</sup>
Solution
First, we need to find the prime factors of 72.
Step 1: Start by dividing the number by the smallest prime number, which is 2. 72 ÷ 2 = 36.
Step 2: Continue this process. 36 ÷ 2 = 18.
Step 3: Continue dividing by 2. 18 ÷ 2 = 9.
Step 4: Now, 9 cannot be divided evenly by 2, so we move on to the next prime number, which is 3. 9 ÷ 3 = 3.
Step 5: Finally, 3 ÷ 3 = 1.
So, the prime factors of 72 are 2, 2, 2, 3, and 3.
In index notation, this is written as 2^3 × 3^2.
Therefore, the correct answer is A: 2^3 × 3^2.
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