Number Properties Flashcards
An integer is divisible by 4 if
The last two digits are divisible by 4
An integer is divisible by 3 if
The sum of its digits is divisible by 3
An integer is divisible by 6 if
It is divisible by both 2 and 3
An integer is divisible by 8 if
The last 3 digits are divisible by 8
An integer is divisible by 9 if
The sum of the integers digits is divisible by 9
Given that integer n is divisible by 3,7 and 11, what other factors must be divisors of n?
N must also be divisible by all possible products of 3, 7 and 11:
21, 33, 77, and 231
What is the least common multiple of 18 and 24?
72
If the sum or product of two primes is even…
One of the numbers must be 2
Algebraic form of even number
2n
n = any integer
Algebraic form of odd number
2n + 1 or 2n - 1
Is zero a digit?
Is zero even?
Is zero an integer?
0! = ?
Zero is a digit
Zero is an even integer
0! = 1
Remainder formula
(5/2) = 2 + (1/2)
Dividend/Divisor = Quotient + (Remainder/ Divisor)
First 10 prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Standard set of numbers for testing
Every integer and half integer btw -2 and 2:
{-2,-3/2,-1,0,1/2,1,3/2,2}
(Even) + (even) =
Even
(Odd) + (odd) =
Even
(Even) + (odd) =
Odd
(Even) x (even) =
Even
(Odd) x (odd) =
Odd
(Even) x (odd) =
Even
If two numbers have no primes in common (greatest common factor and least common multiple)
then their GCF is 1 and their LCM is simply their product
First multiple of any number
Is zero.
If a + b is even, what is ab?
Cannot be determined.
A and b are both even or both odd
If c,d,e are consecutive integers, what is cde?
Even (group must have at least one even)
Molly is rolling a number cube cube with faces 1 to 6. She will stop when she receives a 1. What is probability that Molly will roll the die less than 4 times before stopping?
91/216
Six people are going to the movies together and will sit in 6 adjacent seats. If two of them will not sit next to each other, in how many arrangements can the six ppl sit?
Use glue method.
First, ignore constraint: 6! = 720
Imagine 2 ppl are stuck together, now effectively 5 ppl. 5! = 120
Multiply by 2 to account for order =240
720 - 240 = 480
What is the greatest integer k for which 3^k is a factor of p? Translation:
…how many 3’s are there in p?
Order least to greatest:
.345
Sq rt (.346)
(.345)^2
Smallest: (.345)^2
2nd: .345
Largest: sq rt (.345)
