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# What is a test for finding a prime number?

Updated: 12/20/2022

Wiki User

14y ago

Divide it by prime numbers that are less than or equal to the square root of the number. If any of the smaller prime numbers evenly divide into the original number, then the original number is not prime. Otherwise, the original number is prime.

Example: Determine if 253 is prime.

Solution: First determine that the square root of 253 is about 15.9. So we check all the prime numbers less than or equal to 15 (namely: 2, 3, 5, 7, 11, and 13) to see if any of them evenly divide into 253. The number 11 does divide evenly into 253, so 253 is not prime.

Example: Determine if 659 is prime.

Solution: The square root of 659 is about 25.7, so we check all the prime numbers less than or equal to 25 (namely: 2, 3, 5, 7, 11, 13, 17, 19, and 23) to see if any of them evenly divide into 659. None of them do, so 659 is prime.

Example: Determine if 1073 is prime.

Solution: The square root of 1073 is about 32.8, so we check all the prime numbers less than or equal to 32 (namely: 2, 3, 5, 7, 11, 13, 17,19, 23, 29, and 31) to see if any of them evenly divide into 1073. The number 29 does, so 1073 is not prime.

TIP: When dividing large numbers by the smaller prime numbers there are easy ways to see if some are divisible without a calculator.

If the number is even it is divisible by 2.

If the digits in it add up to a number that is divisible by three than it is divisible by 3.

ex. 234 2+3+4 = 9, and 9 is divisible by 3. So 234 is also divisible by 3.

If the number ends in 0 or 5 it is divisible by 5.

To test for divisibility by 11, alternately add and subtract each digit in the number. If the result is divisible by 11, then the original number is divisible by 11; otherwise it is not.

ex. 43,795,293,718 is divisible by 11, since if you add 4 (starting of course at zero), then subtract 3, then add 7, then subtract 9, then add 5, then subtract 2, then add 9, then subtract 3, then add 7, then subtract 1, and finally add 8, the result is 22, which is divisible by 11.

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14y ago

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Related questions

### When finding the factor of 841 what is the largest factor you would test?

When finding the factors of 841, the largest number you would test is 29. No prime number higher than 29 could be a factor because the square of that number would exceed 841.

### What is finding the factors of a number that are all prime?

That's finding the prime factorization.

### When finding the factors of 841 what is the largest factor you would have to test and what theorem supports it?

When finding the factors of 841, the largest number you would test is 29. No prime number higher than 29 could be a factor because the square of that number would exceed 841.

### What is the difference between finding the factors of a number and finding the prime factors of a number?

No difference. Once you've found the factors of a number, the prime numbers on that list are the prime factors.

### How is prime factorization different from finding factors of a number?

All numbers have factors. Some factors are prime numbers, some are composite numbers, one is neither. When finding the factors of a number, you find all the factors. The prime factorization is a multiplication string of just prime factors that will total the given number.

### What is the formula for finding a prime number?

Any number that has only two factors is a prime number.

### What is the greatest number to test whether 2558 is prime?

If its divisible by 2 then it's not a prime number. But 2 by itself is a prime number

### What is the definition prime factorization?

Prime Factorization is finding which prime numbers multiply together to make the original number.

### What are the prime factorization for composite numbers 1-100?

finding the prime factors of a composite number

### What is the greatest prime you must consider to test whether 854 is a prime number?

You only need to test numbers up to the last prime number equal to or less than the square root of a number when testing whether it is prime. The square root of 854 is between 29 and 30, so you would test up to the prime number 29.

### What is the greatest prime number to test if 6330 is a prime number?

Divide it with primes less than half of the number.

### Can decimals be prime?

on my test it said is 1.68 a prime number i sed yes but it was no :(