Example: the only factors of 13 are 1 x 13, so 13 is a prime number
Example: the number 12 has several factors ( 1 x 12 2 x 6 3 x 4), so 12 is a composite number
As the video version of the Sieve of Eratosthenes shows, to find out if a number less than 100 is a prime number, we only have to check to see if it has any of these factors: 2, 3, 5, or 7. If none of these is a factor of the number we are looking at, then that number is a prime number.
To see if 2 is a factor of a number, just determine if that number is even. Even numbers have 2 as a factor, so an even number cannot be prime (except for 2 itself, because the only factors of 2 are 1 and 2.
64 is an even number (you can tell because it has an even number in the ones place), therefore 2 is a factor of 64. The number 64 is not a prime number because it has at least one other factor besides 1 and 64.
To see if 5 is a factor of a number, simply look at the ones place. If a number has a 0 or a 5 in the ones place, that number has 5 as a factor and cannot be a prime number.
75 has 5 as one of its factors. You can tell by looking at the ones place and seeing a 0 or 5. Therefore 75 is not a prime number because it has at least one other factor besides 1 and 75.
To see if 3 is a factor of a number, use a simple trick: add up the digits of the number and determine if that sum is a multiple of 3. For example, you want to see if the number 87 has 3 as one of its factors.
8 + 7 = 15, and the sum (15) is a multiple of 3. Therefore this trick tells us that 87 is not a prime number because it has at least one other factor besides 1 and 87.
To see if 7 is a factor of a number, the easiest way is to skip-count or make a list of the multiples of 7.
7 itself is a prime number but all of its multiples are composite because they have 7 as a factor.
14 21 28 35 42 49 56 63 70 77 84 91 98
If you go through the steps to determine if 2, 3, and 5 are factors of a given number, you would have already found factors of the bolded numbers above. That leaves just 49, 77, and 91 to add to a list of numbers that are not prime because they have at least one factor other than 1 and itself.