Official Guide Explanation:
Problem Solving #159




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Solution and Metadata

Question: 159
Page: 175
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples
Category 2: Arithmetic > Properties of Integers > Primes

Explanation: To find the answer, we'll need to start by factoring 7,150.

7150 = 715(10), so we know 10 is a factor, meaning that 2 and 5 are prime factors. Now focus on 715.

715 = 5(143). We already know that 5 is a prime factor, so we can focus on 143.

You may not recognize 143 as having smaller prime factors. In cases like that, check the slightly larger primes, such as 7 and 11. 140 is a multiple of 7, so 143 is not; we can establish that 7 is anot a factor. 11, however, is a factor. Since 121 is 112, we can count by 11's to fin that 132 is 11(12), and 143 is 11(13). Both of those factors are prime, so we know that there are two more prime factors. We also know that there aren't any more factors, since we've found that:

715 = 2 * 5 * 5 * 11 * 13

That's four prime numbers that are factors of 7150. Choice (D) is correct.

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