Let’s start this lesson with a basic lesson in divisibility.

**Divisibility rules – you should memorize these! A number is divisible by…**

- by 2 if the number is even or ends in 2,4,6,8 or 0 (this should be obvious)
- by 3 if the sum of the digits is divisible by 3. Example: the number 43215 is divisible by 3 because 4+3+2+1+5 = 15 and 15 is divisible by 3. The number is 3229 is not divisible by 3 because 3+2+2+9 = 16 and 16 is not divisible by 3.
- by 4 if the last two digits are divisible by 4
- by 5 if the last digit is a 5 or 0.
- by 6 if a number is divisible by both 2 and 3
- no easy rule for 7.
- if the last three digits are divisible by 8
- if the sum of the
- digits is divisible by 9. (Example: 2349 is divisible by 9 because 2+3+4+9= 18 and 18 is divisible by 9)
- by 10 if the last digit is 0.

**Moving on to Prime Numbers**

Prime numbers are pretty cool. They are the building blocks of numbers and they can tell us a lot about numbers. They also happen to be an important concept on GMAT math questions.

**Facts about Prime Numbers**

**Prime Factorization (Getting to the Building Blocks of Numbers)**

To prime factorize a number (i.e. express a number as a product of primes), divide the number by factors, putting the divisor on one branch and the quotient on the other until only primes are left: Example: prime factorization of 48.

Notice it doesn’t matter which factor we start the division with. The end result is the same.

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