The prime factors of a number, n, can be listed. For example, the prime factors of 12 are 2, 2, 3, as 12 = 2 × 2 × 3. For which of the following integers is the mode, of the prime factors, 5? A. 440 B. 512 C. 620 D. 740 E. 750
(E) To solve this question we will evaluate each number (A) 440 = 2 × 2 × 2 × 5 × 11, the mode of the prime factors, 2, 2, 2, 5, 11, is 2. (B) Since 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2, the mode of the prime factors is 2. (C) Since 620 = 2 × 2 × 5 × 31, the mode of the prime factors (2, 2, 5, 31) is 2. (D) Since 740 = 2 × 2 × 5 × 37, the mode of the prime factors (2, 2, 5, 37) is 2. (E) Since 750 = 2 × 3 × 5 × 5 × 5, the mode of the prime factors (2, 3, 5, 5, 5) is 5. 
The key with this question is trying to decide which one to do first. 750 = 250 × 3. We know that any number which is 5 squared is what you should start with. The same would hold true if you had a question asking about the number of factors of 2. A square based on 2 such as 64 would have more than a number that had 2s and 3s.
