Download Notes – Number of the Day

Notes – Number of the Day
prime number – a number whose only factors are itself and 1.
Ex: 5 is a prime number.
The factors of 5 are 1 and 5.
composite number – a number that has more than one proper
factor
Ex: 10 is a composite number.
The factors of 10 are 1,2, and 5.
factors - numbers multiplied together to get a product
Ex: 1, 2, 5 and 10 are factors of 10.
*Factors of a number must be equal to or less than the
number.
proper factors of a number – all the factors of a number except
for the number itself
Ex: factors of 10 – 1, 2, 5, 10
proper factors of 10 – 1,2,5
common factor factors that are shared by two or more numbers
Ex: factors of 10 – 1, 2, 5, 10
factors of 30 – 1, 2, 3, 5, 6, 10, 15, 30
common factors of 10 and 30 – 1, 2,5, 10
Greatest Common Factor – The largest factor shared by two or
more numbers
Ex: the GCF of 10 and 30 is 10
multiples of a number – products of that number and another
number. Multiples of a number make up the multiplication
table for that number.
Ex: multiples of 10 – 10, 20, 30, 40…
*Multiples of a number must be equal to or greater than the
number.
common multiples – multiples that are shared by two or more
numbers
Ex: multiples of 10 – 10, 20, 30, 40…
multiples of 5 - 5, 10, 15, 20, 25, 30, 35, 40…
common multiples of 10 and 5 – 10, 20, 30, 40…
Least Common Multiple – The smallest multiple that is common to
two or more numbers
Ex: LCM for 10 and 5 is 10.
abundant number – any number whose proper factors add up to
more than the number itself
Ex: 12 is an abundant number.
 proper factors of 12 – 1, 2, 3, 4, 6,
 1 + 2 + 3 + 4 + 6 = 16
 16 > 12
deficient number – any number whose proper factors add up to
less than the number itself
Ex: 10 is a deficient number
 proper factors of 10 – 1, 2, 5
 1+2+5=8
 8 < 10
exponent - A small raised number written to the right of a digit
that tells how many time that digit is used as a factor
factor tree – strategy for finding the prime factorization of a
number
270
10
5
X
X
2
27
3
X
9
3
X
3
prime factorization – the longest factor string for a number made
up of only prime numbers
Ex: The prime factorization for 270 is 2 X 3 X 3 X 3 X 5
3
 The prime factorization with exponents is 2 X 3 X 5
. The digit 3 is used as a factor three times so we
use the exponent 3 .
Divisibility rules
Divisible by 2 – if there is a 2,4,6,8,or 0 in the ones place
Divisible by 3 – if the sum of the digits in the number is a multiple
of 3 then the number is divisible by 3.
Ex: 1344 is divisible by 3 because the sum of the
digits, 1 + 3 + 4 + 4 = 12 and 12 is a multiple of 3.
Divisible by 6 – if the number is divisible by 2 and 3
Divisible by 5 – if there is a 0 or 5 in the ones place
Divisible by 10 – if there is a 0 in the ones place
Using prime factorization to find the GCF
 Find the GCF for 260 and 36
 Make a factor tree for each number to find
each prime factorization.
 PF for 260 = 2 X 2 X 5 X 13
 PF for 36 = 2 X 2 X 3 X 3
 Make a factor string using only the factors
that are shared by both prime
factorizations.
 GCF = 2 X 2 = 4
Using prime factorization to find LCM
 Find the LCM for 260 and 36
 Make a factor tree for each number to find
each prime factorization.
 PF for 260 = 2 X 2 X 5 X 13
 PF for 36 = 2 X 2 X 3 X 3
 Make the shortest factor string which
contains both prime factorizations.
 LCM = 2 X 2 X 3 X 3 X 5 X 13 = 2340