All cards
1
Prime numbers up to 50
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
2
What is prime factorization (write 1 example)
Every positive integer greater than 11 can be written as the product of primes in exactly one way
24=2^3 3^1
100=2^2 5^2
17=17^1
350=2^1 5^2 7^1
24=2^3 3^1
100=2^2 5^2
17=17^1
350=2^1 5^2 7^1
3
how many positive factors does ____ have
ex: 300
1. prime factorize: 2^3 3^1 5^3
2. Add 1 to all exponents: 2^4 3^2 5^4
3. Multiply all exponents: 32
4. 300 has 32 positive factors
1. prime factorize: 2^3 3^1 5^3
2. Add 1 to all exponents: 2^4 3^2 5^4
3. Multiply all exponents: 32
4. 300 has 32 positive factors
4
Integers - natural/counting numbers
numbes you can count (goes up forever)
5
Integers - natural/counting numbers
natural numbers and 0
6
Integers
all whole numbers (and 0) including negative numbers
7
equation to find the integers between 2 numbers
(last - first) + 1
8
find the Sum of integers in an interval ( NOT starting w/1)
- Find the number of integers in the interval
- Calculate the sum of the first and last numbers
- Multiply the numbers from steps 1 and 2 together and divide by 2
- Calculate the sum of the first and last numbers
- Multiply the numbers from steps 1 and 2 together and divide by 2
9
find the Sum of integers in an interval ( starting w/1)
10
Factor finding sysytem
start w 1, go in order until the gap between the numbers being multiplied is as small as possible 
11
Factorials (!)
an integer multiplied by all of the positive integers that come before it EX: 4! = 4x3x2x1
12
is X a factor of Y!
Factors of factorials (!) can be larger than the factorial as long as they follow the rules (can be made out of other factors in the factorial). 
13
Non factors of Factorials or (!)
Prime: Find the prime numbers greater than the factorial
Non-prime: the smallest multiples of the prime numbers greater than the factorial
One prime non-factor of 10! = 11
One non-prime non-factor of 10! = 22
Non-prime: the smallest multiples of the prime numbers greater than the factorial
One prime non-factor of 10! = 11
One non-prime non-factor of 10! = 22
14
Integer divisibility 1
ALL integers are divisable by 1
15
Integer divisibility 2
If it ends in 0,2,4,6,8
16
Integer divsibility 3
If the sum of digits in the integer is divisible by 3
17
Integer divisibility 4
if the sum of the last 2 digits is divisable by 4
18
Integer divisibility 5
An integer is divisible by 5 if the last digit in the number is a 5 or a 0.
19
Integer divisibility 6
An integer is divisible by 6 if it is also divisible by 2 and 3
20
Integer divisibility 8
An integer is divisible by 8 if the last three digits of the number are divisible by 8
*if it ends in 000 it IS divisable by 8
*if it ends in 000 it IS divisable by 8
21
Integer divisibility 9
An integer is divisible by 9 if the sum of the digits of the number is divisible by 9.
22
Integer divisibility 10
An integer is divisible by 10 if the last digit in the number is 0.