Number Properties Flashcards
Even - even
Even
Even - odd
Odd
Odd - odd
Even
Odd - even
Odd
Even + even
Even
Even + odd
Odd
Odd + even
Odd
Odd + odd
Even
Even x even
Even
Even x odd
Even
Odd x odd
Odd
Even/even
Even or odd
Even / odd
Even
Odd / odd
Odd
Prime numbers < 100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Formula for a x b
LCM (a,b) x GCF (a,b)
Divisibility rule for 3
Sum of all digits is divisible by 3
Divisibility rule for 4
Last 2 digits are divisible by 4 or is a multiple of 100
Divisibility rule for 6
Even and sum of digits is a multiple of 3
Divisibility rule for 8
Even and last 3 digits are divisible by 8, or multiples of 1000
Divisibility rule for 9
Sum of all digits is divisible by 9
Divisibility rule for 11
Sum of odd numbered place digits - sum of even place digits is divisible by 11
Divisibility rule for 12
Divisible by 3 (sum of all digits divisible by 3) and 4 (last 2 digits divisible by 4 or multiple of 100)
X(x+1)(x-1) is divisible by
3!
Product of x consecutive integers is divisible by
X!
N^5 - 5n^5 + 4n
5 consecutive integers from (n-2) to (n+2), divisible by 120!
If n is odd, (n-1)(n+1) is divisible by
8
Formula for division and remainders
X/y = Q + r/y
Trailing zeros
5x2 pairs of prime factorization
Units digit of any factorial > or equal to 5!
0 (5x2 pair)
Leading zeros if 0
0
Leading zeros of 10
1
Leading zeros if 100
2
Formula to find leading zeros
If x is an integer with k digits, 1/x will have k-1 leading zeros
Unless x is perfect power of 10, then k-2 leading zeros
Leading zero definition
Zeros to the right of decimal but before first nonzero number
How to know if a decimal terminates
Prime factorization of fraction denominator contains only 2s, 5s, or both
Unit digit pattern of consecutive powers of 2
2,4,8,6
Unit digit pattern of consecutive powers of 3
3,9,7,1
Unit digit pattern of consecutive powers of 4
4,6
Unit digit pattern of powers of 5
All end in 5
Unit digit pattern of powers of 6
All end in 6
Unit digit pattern of consecutive powers of 7
7,9,3,1
Unit digit pattern of consecutive powers of 8
8,4,2,6
Unit digit pattern of consecutive powers of 9
9,1