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What numbers need to be checked to see if 127 is prime or composite?
Check as many as you want, you won't find any divisors. 127 is prime.
What is the largest composite number but less than 200?
Testing the largest whole number less than 200, 199, we find that it is not evenly divisible by 2, 3, 5, 7, 11 or 13. Since the square root of 199 is between 14 and 15, there's no need to test any prime numbers higher than 14. Therefore, the answer is 198, since it is an even number, and all even numbers are composite numbers because they are divisible by 2. A composite number is the opposite of a prime number.
How can you work out prime numbers and composite numbers easily?
AnswerTo test if a number is prime or composite by hand, the easiest thing to do is test if it's divisible by numbers you know to be prime (start with 2, 3, 5, 7, and so on). If none of them divide it, once the numbers you're dividing by get bigger than the square root of the number you're testing (roughly - you don't need to waste time actually calculating the square root), you're done and know it's prime. For example, here's how you'd test if 107 is prime: It's odd, so it's not divisible by 2; It's not divisible by 3 (use the divisibility rule: 1+0+7=8, not 3 or 6 or 9) It's not divisible by 5 (doesn't end in 5 or 0) It's not divisible by 7 (if it were, 107-7=100 would be divisible by 7, which we know isn't true) At this point, we know it's prime, since we'd need to check 11 next. But 11*11=121, bigger than 107, so 11 is greater than the square root of 107. For large numbers, the best thing to do is to use a computer.
How many composite numbers are there from 150 to 200?
To determine the number of composite numbers between 150 and 200, we first need to identify the prime numbers within this range. The prime numbers in this range are 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, and 199. Therefore, the composite numbers between 150 and 200 are all the numbers in this range that are not prime. Counting these numbers, we find that there are 49 composite numbers between 150 and 200.
How do you determine whether a number is prime or composite?
Negative numbers, zero, and one are neither prime nor composite. See the related questions as to an explanation why. See whether the number is divisible by 2, and by all odd numbers up to the square root of the number. For numbers up to 100, it is enough to check the factors 2, 3, 5, and 7. For higher numbers you need to check more factors. For very large numbers (for example, hundreds of digits), more efficient methods are known, but those methods are also more complicated. Check the related link for a number factoring calculator.
