Question

Write the prime factorization. (Skills Review, p. \(T T T\) ) $$72$$

Short answer

The prime factorization of 72 is \(2^3 * 3^2\).

Step-by-step solution

Prime number identification

Recognize what a prime number is. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Start factorization process

Begin this process by dividing 72 by the smallest prime number, which is 2. The result is: \(72 \div 2 = 36\). This means that 2 is a prime factor of 72.

Continue factorization

Continue with the factorization by dividing 36 by the smallest possible prime number. Again it is 2. The result is: \(36 \div 2 = 18\). This means that another 2 is a prime factor of 72.

Onward with the factorization

Do the same process to 18. Dividing it by 2 again gives \(18 \div 2 = 9\). This means another 2 is a prime factor. Now we have three 2's as the prime factors of 72 so far.

Final factorization

Now we try to divide 9. It is not divisible by 2. The next prime number is 3. 9 divided by 3 is 3. This means that both 3's are prime factors of 72 as well.