Factors / Multiples

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ISEE Upper Level Quantitative Reasoning › Factors / Multiples

Questions 1 - 10
1

Which of the following numbers is prime?

Explanation

The correct answer is , and this can be determined in the following manner.

First, find the approximate square root of the number:

We know this because:

Therefore, we only need to consider prime numbers through

Is evenly divisible by any of these numbers? In this case, the answer is no, therefore is prime. Consider the case where the answer is not prime: .

We know this because:

Therefore, we need to consider the followig prime numbers:

Is divisible by any of these numbers? In this case, the answer is yes. is divisible by .

2

Add all of the prime numbers between 20 and 40.

Explanation

The prime numbers between 20 and 40 are 23, 29, 31, and 37.

Their sum is .

3

Which of the following numbers is prime?

Explanation

The correct answer is , and this can be determined in the following manner.

First, find the approximate square root of the number:

We know this because:

Therefore, we only need to consider prime numbers through

Is evenly divisible by any of these numbers? In this case, the answer is no, therefore is prime. Consider the case where the answer is not prime: .

We know this because:

Therefore, we need to consider the followig prime numbers:

Is divisible by any of these numbers? In this case, the answer is yes. is divisible by .

4

Add all of the prime numbers between 20 and 40.

Explanation

The prime numbers between 20 and 40 are 23, 29, 31, and 37.

Their sum is .

5

Which of the following numbers is prime?

Explanation

The correct answer is , and this can be determined in the following manner.

First, find the approximate square root of the number:

We know this because:

Therefore, we only need to consider prime numbers through

Is evenly divisible by any of these numbers? In this case, the answer is no, therefore is prime. Consider the case where the answer is not prime: .

We know this because:

Therefore, we need to consider the followig prime numbers:

Is divisible by any of these numbers? In this case, the answer is yes. is divisible by .

6

Add all of the prime numbers between 20 and 40.

Explanation

The prime numbers between 20 and 40 are 23, 29, 31, and 37.

Their sum is .

7

Let be the set of all integers such that is divisible by and . How many elements are in ?

Explanation

The elements are as follows:

This can be rewritten as

.

Therefore, there are elements in .

8

Let be the set of all integers such that is divisible by and . How many elements are in ?

Explanation

The elements are as follows:

This can be rewritten as

.

Therefore, there are elements in .

9

Let be the set of all integers such that is divisible by and . How many elements are in ?

Explanation

The elements are as follows:

This can be rewritten as

.

Therefore, there are elements in .

10

Find the greatest common factor of 20 and 36.

Explanation

To find the greatest common factor (GCF), you need to determine the factor that both numbers share that is of the greatest value. List the factors of each number and identify the largest number in value that is in both lists:

The GCF of 20 and 36 is 4 since it is the largest number in value that shows up in both lists.

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