ISEE Upper Level Quantitative : Other Factors / Multiples

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

Example Question #41 : Other Factors / Multiples

Which of the following is NOT a factor of ?

Possible Answers:

Correct answer:

Explanation:

First, we must solve for 

While 64 is divisible by 4, 8, and 16, it is not divisible by 7; therefore, 7 is not a factor of 64 and is thus the correct answer. 

Example Question #51 : Numbers And Operations

 and  are distinct odd primes. Which is the greater quantity?

(a) The number of factors of 

(b) The number of factors of 

Possible Answers:

(b) is greater

(a) is greater

(a) and (b) are equal

It is impossible to tell which is greater from the information given

Correct answer:

It is impossible to tell which is greater from the information given

Explanation:

Since  and  are distinct primes, the prime factorization of  is ; therefore, the factors of  are 1, , and . There are four factors.

We show that  may or may not have more factors by example.

Case 1: .

Then , which has four factors: 1, 2, 4, 8.

Case 2: 

Then , which has six factors: 1, 2, 3, 4, 6, 12.

Therefore, we have at least one situation in which  and  have the same number of factors, and at least one in which  has more. The given infomation is insufficient.

Example Question #42 : How To Factor A Number

 and  are distinct odd primes. Which is the greater quantity?

(a) The number of factors of 

(b) The number of factors of 

Possible Answers:

It is impossible to tell which is greater from the information given

(b) is greater

(a) and (b) are equal

(a) is greater

Correct answer:

(a) is greater

Explanation:

Since  and  are distinct primes, the prime factorization of  is ; therefore, the factors of  are 1, , and . There are four factors.

Since  is a prime, the prime factorization of  is ; therefore, the factors of  are 1, , and . There are three factors.

This makes (a) greater.

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