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Please Note:
The last administration of the old SAT was on 1/22/05. Beginning 3/12/05, only the New SAT will be administered. You should be studying the New SAT book. Go there!
The last administration of the old SAT was on 1/22/05. Beginning 3/12/05, only the New SAT will be administered. You should be studying the New SAT book. Go there!
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Multiples, Factors, and Primes
SAT questions on multiples, factors, and primes can be
difficult simply because of all the terminology they so freely throw
around. Below, we give you the definition for these three mathematical
concepts. You don’t have to love them, but you should know them.
Multiples
The multiple of a number is the product generated when
that number is multiplied by an integer. The first five multiples
of 7 are 7, 14, 21, 28, and 35 since 
; 
; The Least Common Multiple
The least common multiple (LCM) is the name given to the
lowest multiple that two particular numbers share. For example,
the multiples of 6 and 8 are:
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, . . .
Multiples of 8:
8, 16, 24, 32, 40, 48, 56, 64, 72, . . .
As the two lists show, 6 and 8 both
have 24 and 48 as multiples (they also
share many other multiples, such as 72, 96,
. . . ) Because 24 is the lowest in value of these
shared multiples, it is the least common multiple of 6 and 8.
Being able to figure out the least common multiple of
two numbers can prove quite handy on the SAT, especially for questions
in which you have to add or subtract two fractions with unlike denominators,
which we’ll explain later in this chapter.
Factors
A factor of a number is the quotient produced when that
number is divided by an integer. For example, 2, 3, 4,
and 6 are all factors of 12 because 
and 
Factors,
then, are related to multiples. A given number is a multiple of
all its factors: 2 and 6 are factors of 12,
so 12 is a multiple of both 2 and 6.
and Factors,
then, are related to multiples. A given number is a multiple of
all its factors: 2 and 6 are factors of 12,
so 12 is a multiple of both 2 and 6.The Greatest Common Factor
The Greatest Common Factor (GCF) of two numbers is the
largest factor that the two numbers share. For example, the GCF
of 18 and 24 is 6, since 6 is
the largest number that is a factor for both 18 and 24.
Primes
A prime number is divisible by only 1 and
itself (the number 1 itself is not considered prime).
For example, 17 is prime because it is divisible by
only 1 and 17. The first few primes, in
increasing order, are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,
41, 43, 47, 53, . . .
Let’s say the SAT asks you whether 91 is
prime. You should try to answer this question by showing that 91 is
not prime. You can do this pretty quickly if you understand the
rules above. Here is the strategic way to check whether 91 is
prime:
- Is 91 divisible by 2? No, it does not end with an even number.
- Is 91 divisible by 3? No, 9 + 1 = 10, which is not divisible by 3. You don’t have to check if 91 is divisible by 4, because you already know that is isn’t divisible by 2. No number that isn’t divisible by 2 will be divisible by 4.
- Is 91 divisible by 5? No, 91 does not end with 0 or 5. You don’t have to check if 91 is divisible by 6, because you already know that is isn’t divisible by 2 or 3.
- Is 91 divisible
by 7? Yes!
91 /7 = 13.
Therefore, 91 is not prime.
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