Basic Properties of Numbers Flashcards
divisibility rules: 2
if the units digit is even
divisibility rules: 3
sum of digits is divisible by 3
ex. 27 , 2+7 = 9 which is divisible by 3
divisibility rules: 4
final two digits are divisible by 4
ex. 316
divisibility rules: 5
units digit of 5 or 0
divisibility rules: 6
- units digit is even
- sum of digits is divisible by 3
divisibility rules: 9
sum of digits is divisibly by 9
divisibility rules: 10
units digit is 0
is zero (0) an even or odd?
even
is zero (0) an integer, yes or no?
yes
is zero (0) a prime number, yes or no?
no
is 1/2 or 0.5 an integer, yes or no?
no
integer
has to be a whole number ex. 3, 4, 89
prime number
- positive integer
- divisible only by itself and 1
is one, 1, an integer? is one, 1, a prime number?
1 is an integer but not a prime number
is 2 an integer, is 2 a prime number?
2 is an integer and 2 is also a prime number
- 2 is the only even prime number and the least prime number
factor vs. multiple
think “factors few, multiples many”
is zero (0), positive or negative?
0 is not positive nor negative
remainder
integer left over when an integer is divided by another
a remainder is always an integer
if integer m is divided by integer n then:
m = (a)(n) + b where a and b are integers and integer b is the remainder
ex. 13/5 where 13=m and 5=n so, 13 = (a)(5) + b then you know a = 2 and b = 3 and 3 is the remainder
divisible
when a number is divisible, it divides evenly
all factors of a number are its divisors
what are the first 5 prime numbers?
2, 3, 5, 7, 11
common factors
factors that two integers share
what is the greatest common factor of 12 and 18?
6
prime factorization
writing an integer as a product of its prime factors
ex. 45
/ \
3 15
/ \
3 5
so the primer factorization of 45 = 3^2 * 5
prime factorization of 72
72
/ \
2 36
/ \
3 12
/ \
3 4
/ \
2 2
= 2^3 * 3^2
multiples
multiples can be positive or negative and multiples of integer n are all the numbers:
0, +- 1 *n, +- 2 *n, +- 3 n, +- 4n
ex. the positive multiples of 4?
= 4, 8, 12, 16, 20, 24…
is 21 a factor OR a multiple of 42?
factor
least common multiple of 6 and 8?
make a list of the multiples of each number until you find a number on both lists
multiples of 6: 6, 12, 18, 24, 30
multiples of 6: 8, 16, 24
least common multiple of 6 and 8 = 24
fractions
ex. there are 5 men and 7 women in a room, what fraction are men?
part/ whole
ex. there are 5 men and 7 women in a room, what fraction are men? = 5/12
comparing fractions to know which one is greater
ex. which is greater 4/7 or 5/9?
use the bow time method if neither the numerator or denominator is the same
4/7 5/9 –> 75 = 35 and 94 = 36 so 4/7 is greater
multiplying fractions
multiply straight across
3/4 x 2/6 = 6/20 = 3/10
dividing fractions
9/5 divided by 7/10 = ?
flip the second fraction then multiply
9/5 * 10/7 = 18/7
what is the reciprocal of 1/ (1/4)?
= (1/4)/1 = 1/4
Adding and subtracting fractions if the denominators are the same
just add or subtract the numerator and keep the denominator then simplify
Adding and subtracting fractions if the denominators are not the same
7/12 + 1/3
use bowtie method to add or subtract!
7/12 + 1/3 = (21 + 12)/ 36 = 33/36
how many distinct factors of 36 are there?
36
/ \
1 36
2 18
3 12
4 9
6 6
= 9 distinct factors
How do you know when a factor list is done?
When there are no numbers between the last two factors that divides evenly into the number you are factoring
How many integers between 100 and 300 are multiples of both 3 and 7?
answer = 10
3 and 7 are both prime numbers and 3 x 7 = 21. The only numbers that will be divisible by 3 and 7 are multiples of 21
so 21: (times these numbers is between 100 - 300 x 5 x 10 x 6 x 11 x 7 x 12 x 8 x 13 x 9 x 14
QA: The number of positive integers that are both factors of 48 and multiples of 4
QB: 5
A B C D
Answer = A
4 is a multiple of 4 so there are six values that re factors and multiples
The incoming class in a college can be divided up evenly into 18, 20, 24, or 36 lecture halls. Which could be the number of students in the incoming class? Select all that apply
180 360 480 720 960 1080 1440
answers = A, B , F, G
PRIME FACTOR - any correct answer must be divisible by all of the prime factors
also if one of the options is divisible by an answer that was correct, it will also work. Aka 1080 and 1440 are divisible by 360 which we showed to be true so they will work too
What is the difference between the product of the distinct prime factors of 84 and the sum of the distinct prime factors of 192 ?
answer = 37
How can 10^3 be rewritten?
5^2 x 2^3
x, y, and z are negative integers, and -(x/y) = z
QA: x^2
QB: yz
Answer = D cannot be determined!
do not forget to try 1 as a number!!
The remainder when 10 is divided by positive integer x is y for all values of y > 0. If the remainder when 11 is divided by x is y^2 + 1, then which of the following could be the value for x?
5 6 7 8 9
answer = 9
when 10 is divided by 9 the remainder is 1
when 11 is divided by 9 the remainder is 2 which is = 1^2 + 1
