Which of the numbers is a prime number?
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Which of the numbers is a prime number?
To determine which number is a prime number, we will check each choice for primality based on whether it has divisors other than 1 and itself:
Given these observations, the only prime number among the choices is .
Which of the numbers is a prime number?
If a number has a factor larger than its square root, it must also have a factor smaller than the square root! For 17, , so checking 2, 3, and 4 is enough.
No, 1 is not prime! Prime numbers must have exactly two factors: 1 and themselves. Since 1 only has one factor (itself), it doesn't qualify as prime.
Look for quick tests: Even numbers (except 2) are not prime, numbers ending in 5 (except 5) are not prime, and use divisibility rules for 3, 7, 11, etc.
16 = 2 × 8 = 4 × 4, so it has many factors (1, 2, 4, 8, 16). But 17 cannot be divided evenly by any number except 1 and 17, making it prime.
Most primes (except 2 and 3) are one number away from multiples of 6, like 6±1. For example: 17 = 18-1, and 18 is a multiple of 6!
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