FACTORS
Factors are the numbers being multiplied to reach a product. In the number model, 7 x 6 = 42, the factors are 7 and 6, while the product is 42.
A factor list is all the possible factors of a number. There are 8 possible factors for the number 24 listed below.
24: 1, 2, 3, 4, 6, 8, 12, 24
There are 12 factors for the number 60 listed below.
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
DIVISIBILITY
Divisibility is the ability of a number to be divided evenly by another number. We can say that the number 27 is divisible by 3 because 3 goes into 27, 9 times without any left over (remainder). The following are divisiblity rules for some common one digit numbers.
Divisible by: If:
2 The lasts digit is even
3 The sum of the digits is divisible by 3
4 The last two digits form a number divisible by 4
5 The number ends in 0 or 5
6 The number is divisible by 2 and 3
8 The last three digits form a number divisible by 8
9 The sum of the digits is divisible by 9
Example:
4,836
Divisible by 2 because it ends with a 6 which is an even number
Divisible by 3 because 4+8+3+6= 21 and 21 is divisible by 3 (3*7=21)
Divisible by 4 because the last two digits, "36" is divisible by 4 (4*9=36)
NOT divisible by 5 because the last digit "6" is not 0 or 5
Divisible by 6 because the number is divisible by 2 and 3
NOT divisible by 8 because the last three digits "836" is not divisible by 8
NOT divisible by 9 because the sum of the digits = 21 and not divisible by 9
Make up your own numbers and try the divisiblity rules!
PRIME & COMPOSITE NUMBERS
Prime numbers are numbers greater than one that have exactly only 2 factors - 1 and the number itself. Any number with more than 2 factors is a composite number.
Examples: 2: 1, 2 therefore 2 is a prime number
7: 1, 7 therefore 7 is a prime number
9: 1, 3, 9 since there are more than two factors, 9 is a composite number
23: 1, 23 therefore 23 is a prime number
27: 1, 3, 9, 27 since there are more than two factors, 27 is a composite number
The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
**Mathemeticians have agreed that the number 1 is neither prime nor composite.
"Goldbach's Conjecture"
Every even number greater than two can be written as the sum of two prime numbers.
Ex: 68= 31 + 37 or 34= 31 + 3 or 60=23 + 37
SQUARE & SQUARE ROOT
A square array is an array in the shape of a square, with equal rows & columns. The number represented by a square array is called a square number.
EX: 16 is a square number because it can be represented by 4 rows and 4 columns.
36 is a square number becuase it can be represented by 6 rows and 6 columns.
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