Kaplan Nursing Entrance Practice Exam

How do you find the prime factorization of the number 36?

1. By dividing it by 2 repeatedly

2. By identifying factors that multiply to 36

3. By adding all of its factors

4. By subtracting the largest prime factor

The correct answer is: By identifying factors that multiply to 36

Finding the prime factorization of a number involves expressing that number as the product of its prime factors. The choice that states identifying factors that multiply to 36 is correct because it emphasizes the process of breaking down the number into factors and further into primes. To obtain the prime factorization of 36, one can first find pairs of factors (like 1 x 36, 2 x 18, 3 x 12, and 4 x 9). Among these pairs, you would identify the prime factors: 2, 3, and then continue breaking them down until all factors reach the prime numbers. For 36, this process leads to the factorization of 2 x 2 x 3 x 3, or more concisely, \(2^2 \times 3^2\). The other choices do not represent appropriate methods for finding prime factorization. Continuously dividing by 2 until no longer possible, for instance, may lead you to 9 and then require further breakdown to reach the primes but is not a comprehensive method. Adding all factors does not yield factorization but rather a sum unrelated to prime factors. Subtracting the largest prime factor is also not a strategy related to finding prime