SAT Math : Integers
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Example Questions
Example Question #61 : Factors / Multiples
If 
4
5
3
7
6
5
We will essentially have to represent 180 as a product of prime factors, because 2, 3, 5, and 7 are all prime numbers. The easiest way to do this will be to find the prime factorization of 180.
180 = 18(10)= (9)(2)(10) = (3)(3)(2)(10)=(3)(3)(2)(2)(5) = 
In order for 
The answer is 5.
Example Question #11 : How To Factor A Number
What is the product of the distinct prime factors of 24?
The prime factorization of 24 is (2)(2)(2)(3). The distinct primes are 2 and 3, the product of which is 6.
Example Question #12 : How To Factor A Number
How many prime factors does 
Since 7 is prime, its only prime factor is itself.
Example Question #301 : Arithmetic
What is the smallest positive multiple of 12?
Multiples of 12 are found by multiplying 12 by a whole number. Some examples include:
Clearly, the smallest positive value obtainable is 12. Do not confuse the term multiple with the term factor!
Example Question #31 : Factors / Multiples
How many prime factors of 210 are greater than 2?
one
three
two
four
five
three
Begin by identifying the prime factors of 210. This can be done easily using a factoring tree (see image).
The prime factors of 210 are 2, 3, 5 and 7. Of these factors, three of them are greater than 2.
Example Question #32 : Factors / Multiples
How many integers between 50 and 100 are divisible by 9?
8
7
6
9
5
6
The smallest multiple of 9 within the given range is 
The largest multiple of 9 within the given range is 
Counting the numbers from 6 to 11, inclusive, yields 6.
Example Question #14 : Other Factors / Multiples
Example Question #1 : How To Find Consecutive Integers
The sum of three consecutive even integers is 108. What is the largest number?
36
40
42
38
34
38
Three consecutive even integers can be represented by x, x+2, x+4. The sum is 3x+6, which is equal to 108. Thus, 3x+6=108. Solving for x yields x=34. However, the question asks for the largest number, which is x+4 or 38. Please make sure to answer what the question asks for!
You could have also plugged in the answer choices. If you plugged in 38 as the largest number, then the previous even integer would be 36 and the next previous even integer 34. The sum of 34, 36, and 38 yields 108.
Example Question #1 : Consecutive Integers
The sum of three consecutive even integers equals 72. What is the product of these integers?
17472
13800
12144
10560
13728
13728
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
Example Question #1 : How To Find Consecutive Integers
Four consecutive integers have a mean of 9.5. What is the largest of these integers?
13
12
9
8
11
11
Four consecutive integers could be represented as n, n+1, n+2, n+3
Therefore, by saying that they have a mean of 9.5, we mean to say:
(n + n+1 + n+2 + n+ 3)/4 = 9.5
(4n + 6)/4 = 9.5 → 4n + 6 = 38 → 4n = 32 → n = 8
Therefore, the largest value is n + 3, or 11.
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