How do you tell if a number is prime or not?

Answer 1

A Prime number is one that has only two factors: one and itself.

You can tell if a number is prime quickly by using the Laws of Divisibility:

• Numbers that end in 0, 2, 4, 6, and 8 are divisible by 2.

• If the sum of a number's digit is divisible by 3, the number itself is divisible by 3.

• If the last two digits of a number are divisible by 4, the number itself is divisible by 4.

• If a number ends in 0 or 5, it is divisible by 5.

• If a number is divisible by both 2 and 3, it is divisible by 6.

• If you double the last digit and subtract it from the rest of the number and the answer is 0 or divisible by 7, it is divisible by 7. For example, 4364: 4 doubled is 8. 436 - 8 = 424. You still cannot readily tell if the number is divisible by 7, so you can do it again: 4 doubled is 8. 42 - 8 = 34. 34 is not divisible by 7 so 436 is not divisible by 7

• If the last three digits of a number are divisible by 8, the number itself is divisible by 8.

• If the sum of the digits of a number is divisible by 9, the number itself is divisible by 9.

• If a number ends with 0, it is divisible by 10.

• If you add every other digit and then subtract the rest of the digits and the answer is 0 or is divisible by 11, the number itself is divisible by 11. For example: 1364: 1+ 6 = 7 and 7 - 3 - 4 = 0. The number is divisible by 11.

• If the number is divisible by 3 and 4, it is divisible by 12.

There are more divisibility rules that can be used for large numbers.