# Number Properties

## 40 terms

### divisible by 3

sum of the digits is divisible by 3

### divisible by 9

if the sum of the digits is divisible by 9

### primes from 1 to 41

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41... all primes thereafter will have a units digit of 1, 3, 7, or 9.

### prime

a positive integer with exactly 2 factors

### least common multiple

product of all primes of the product of the numbers. Make a venn diagram of the primes of each number and then multiply the numbers seen in the diagram.

### definition of even

numbers divisible by 2 (which includes 0)

+/- DOE: OEE

+/- DOE: OEE

+/- DOE: OEE

x DOE: EOE

x DOE: EOE

x DOE: EOE

### quotient of 2 odds, 2 evens, or an odd or even

can be either odd or even, cannot be determined

### sum of an evenly spaced set

mean * # in a set

### number of integers in a set

(last number - first number) / incement + 1

list

### is the sum of k integers divisible by k?

yes if the amount of numbers in the set is odd, but it does not equal an integer if the amount is even.

### sum of the 2nd half of a set of consecutive numbers

amount of numbers in half the set to the power of the same

### the sum or difference of a multiple and non-multiple of N

non-multiple of N

### Strategy to find GCF and LCM

To find GCF and LCM, use prime columns. Use prime boxes to find the prime numbers, and then list them to a power in their column. EX:
Number: 2 5 7
100 2^2 5^2 -
140 2^2 5^1 7^1

GCF = smallest count in any column: 2^2 * 5^1 = 20
LCM = highest count in any column: 2^2 5^2 7^1 = 700

### the product of the GCF and the LCM of m and n

equals the product of m and n

n

### product of an evenly spaced set

multiply them all or change them into primes and then exponents to make it easier

always even

### number of factors of a perfect square

always odd, and vice versa

### strategy for remainder problems

choose smart numbers

### remainder as a decimal

Simplify as a fraction. The numerator of the fraction is a prime multiple of the number that is being divided; therefore, the remainder must be a multiple of its smallest prime.

### maximum number of prime factors less than an integer

2^x less than integer. Multiply 2's until you get the closest to the integer.

### When adding/subtracting to a factorial equals a number that cannot be prime

the additional number has some factors that are the same within the factorial.

### maximum length of a number less than a given integer

multiply 2 until the number gets close but does not surpass the integer

### when xy is less than 0, absolute value of (y) - absolute value of (x) =

absolute value of (x + y)

2

### arbitrary numbers when x and y have reversed digits

x = 10a + b; y = 10b + a

2n + 1

2n

### strategy for odds and evens questions

use scenario table

### remainder when divided by 2

odds R1, evens R0

### remainder when divided by 4

odds R1 or R3, evens R0

never an integer

even

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