Math - Even Odd Divisibility

Rules for Adding (Sums) Even and Odd Numbers

Even + Even = Even Odd + Odd = Even Even + Odd = Odd Odd + Even = Odd

Rules for Multiplying (Products) Even and Odd Numbers

Even x Even = Even Odd x Odd = Odd Even x Odd = Even Odd x Even = Even

Odd Numbers

Integers that CANNOT be evenly divided by 2. A number that ends in 1, 3, 5, 7, or 9. All the numbers that are NOT multiples of 2.

Even Numbers

Integers that can be evenly divided by 2. A number that ends in 0, 2, 4, 6, or 8. All the multiples of 2.

Composite Numbers

Numbers that have more than two factors. Ex. 18 is a ___________ number because there are more than two numbers you can multiply together to get 18. It has six factors: 1 x 18, 2 x 9, 3 x 6.

Prime Numbers

Numbers that only have two factors: 1 and itself. Ex. 17 is a _______ number because the only numbers you can multiply together to get 17 are 1 x 17.

Multiples

Numbers you get after multiplying a number by another integers. Ex. 3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12, 3 x 5 = 15 So. . . 3, 6, 9, 12, and 15 are all __________ of 3 because we got them by multiplying 3 times other integers.

Factors

Numbers you multiply together to get another number. Ex. 4 and 6 are __________ of 24 because you multiply them together to get 24.

Greatest Common Factor GCF

The biggest whole number that is a factor of two numbers. Ex. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. 6 is the biggest whole number that is a factor for both of them, so 6 is the _______ of 12 and 18.

Least Common Multiple LCM

The smallest whole number (not including zero) that is a multiple of two numbers. Ex. The first five multiples of 3 are 3, 6, 9, 12, and 15. The first five multiples of 4 are 4, 8, 12, 16, and 20. 12 is the smallest whole number that is a multiple of both of them, so 12 is the ______ of 3 and 4.

Divisibility Rule for 7 (Not required to memorize this one)

To find out if a number is divisible by seven, take the last digit and double it, then subtract it from the rest of the number. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again. Ex: Check to see if 203 is divisible by 7. Double the last digit: 3 x 2 = 6 Subtract that from the rest of the number: 20 - 6 = 14. Check to see if the answer is divisible by 7. 14 is divisible by 7, so 203 is also divisible by 7.

Prime Factorization

When a number is written as the product of all its prime factors.

Divisibility Rule for 10

A number is divisible by 10 if it ends in a zero. Ex. 7,569,430 end is a zero, so it is divisible by 10.

Divisibility Rule for 2

A number is divisible by 2 if it ends in a 0, 2, 4, 6, or 8. All even numbers are divisible by 2. Ex. 6,938: Ends in an 8 so it is divisible by 2.

Divisibility Rule for 3

A number is divisible by 3 if the sum of the digits is divisible by 3. Ex. 93: The sum of the digits 9 + 3 is 12. 12 is divisible by 3, so 93 is divisible by 3.

Divisibility Rule for 4

A number is divisible by 4 if the last two digits are a number that is divisible by 4. (Odd numbers won't work, but must test even numbers) Ex. 7,936: The last two digits are 36. 36 is divisible by 4, so 7,926 is divisible by 4.

Divisibility Rule for 5

A number is divisible by 5 if it ends in a 0 or 5. Ex. 6,975: Ends in a 5, so it is divisible by 5.

Divisibility Rule for 6

A number is divisible by 6 if it is even AND the sum of its digits is divisible by 3. Ex. 114: It is an even number and the sum of its digits 1+1+4 = 6 is divisible by 3, so 114 is divisible by 6.

Divisibility Rule for 8

A number is divisible by 8 if the last three digits are divisible by 8. (Odd numbers won't work, but must test even numbers) Ex. 67, 536: The last three digits make the number 536. 536 is divisible by 8 ( 536 ÷ 8 = 67) so 67,536, is also divisible by 8.

Divisibility Rule for 9

A number is divisible by 9 if the sum of the digits is divisible by 9. Ex. 7,209: The sum of the digits 7 + 2 + 0 + 9 = 18. 18 is divisible by 9, so 7,209 is also divisible by 9.