GRE Math : Prime Numbers
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Example Questions
Example Question #82 : Arithmetic
Which statement is false about prime numbers?
Every positive integer except for 1 is a prime or a product of primes.
There are no negative primes.
Every integer greater than 1 has a unique prime factorization.
None are false.
All are false.
None are false.
All of these statements are true. Let's go through them.
1. There are no negative prime numbers. This appears as if it might be false, but in fact, the prime numbers are defined as whole numbers greater than one that are divisible by only one and itself.
2. Every number except 0 and 1 is a prime number or product of primes. This is also true. Let's look at the factorization of a number that isn't prime. For example, 6 = 2 * 3, which is a product of primes. 12 = 2 * 2 * 3, which is also a product of primes.
3. Every number has a unique prime factorization. We just saw that every number is either prime, or a product of primes. Therefore each number must have a unique prime factorization. Just as above, 6 is the product of two primes, 2 and 3. No other number can be made by mulitplying 2 * 3. The same is true for 12. When we multiply 2 * 2 * 3, the only number we will ever get is 12.
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