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SAT Math : How to find out if a number is prime

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Example Questions

Example Question #11 : Prime Numbers

What's the fourth smallest prime number?

Possible Answers:

Correct answer:

Explanation:

The order of the prime numbers start from 2, 3, 5, 7, 11, 13 . is not prime as it's a unit. is a composite number. So our fourth smallest prime number is .

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Example Question #742 : Arithmetic

Which is not prime?

Possible Answers:

Correct answer:

Explanation:

Since all the numbers are odd and don't end with a , let's check the basic divisbility rule. The divisibility rule for is if the digits have a sum divisible by , then it is.

39=3+9=12

31=3+1=4

37=3+7=10

43=4+3=7

53=5+3=8

Based on this analysis, only is divisible by and therefore not prime and is our answer.

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Example Question #13 : Prime Numbers

Say is a prime number. Which operation could possibly also lead to a prime number?

Possible Answers:

$\textup{Exponents}$

$\textup{Subtraction}$

$\textup{Square root}$

$\textup{Division}$

$\textup{Multiplication}$

Correct answer:

$\textup{Subtraction}$

Explanation:

Prime numbers are integers. So doing division and square roots will not generate integers. By doing multiplication and exponents, we involve more factors. The only possibility is subtraction. If was and we subtracted we get which is also prime.

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Example Question #12 : Prime Numbers

Say is a number. has, other than one and itself, only prime factors. is not a perfect square. What is the smallest prime number can be?

Possible Answers:

Correct answer:

Explanation:

Other than the number itself and one, we also need to have prime factors in that number. Since it's not a perfect square, we need to find the smallest possible prime numbers. That will be 2*3 or which is our answer.

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Example Question #12 : Prime Numbers

Which of the following is not prime?

Possible Answers:

983

787

687

853

691

Correct answer:

687

Explanation:

Since all the numbers are odd and don't end with a , let's check the basic divisbility rule. The divisibility rule for is if the digits have a sum divisible by , then it is.

687=6+8+7=21

787=7+8+7=22

853=8+5+3=16

983=9+8+3=20

691=6+9+1=16

Based on this analysis, only 687 is divisible by and therefore not prime and is our answer.

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Example Question #44 : Factors / Multiples

What's the largest prime number less than 100 ?

Possible Answers:

Correct answer:

Explanation:

Let's work backwards. All even numbers are not prime so we skip . is clearly divisible by . is definitely a composite number as it's divisible by . is divisible by because of the divisibility rule (93=9+3=12) . is divisbile by . The divisibility rule for is double the last digit and subtract from the rest (91=9-1*2=7) . From the remaining answers, is prime and is the largest prime number under 100 and is our answer.

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Example Question #13 : Prime Numbers

Which is prime?

Possible Answers:

132

101

121

Correct answer:

101

Explanation:

This will require us to know the divisibility rule of . The reason for this choice is that some of the numbers are palindromes like so we eliminate 77, 99 . For the three digit numbers, the divisibility rule for is add the outside digits and if the sum matches the sum then it is divisible. Let's see.

$101=1+1\neq0$

121=1+1=2

132=1+2=3

Based on this test, 101 is not divisible by and is our answer.

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Example Question #11 : How To Find Out If A Number Is Prime

If $p$ is a prime number, what could also be prime?

Possible Answers:

$p^{2}$

$3p$

$2p$

$p-2$

Correct answer:

$p-2$

Explanation:

Plug in a prime number such as and evaluate all the possible solutions. Note that the question asks which value COULD be prime, not which MUST BE prime. As soon as your number-picking yields a prime number, you have satisfied the "could be prime" standard and know that you have a correct answer.

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SAT Math : How to find out if a number is prime

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : Prime Numbers

Example Question #742 : Arithmetic

Example Question #13 : Prime Numbers

Example Question #12 : Prime Numbers

Example Question #12 : Prime Numbers

Example Question #44 : Factors / Multiples

Example Question #13 : Prime Numbers

Example Question #11 : How To Find Out If A Number Is Prime

All SAT Math Resources

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