Chapter 9 Number Properties

Question 1

The integer values that divide evenly into that number.

Answer 1

Factors (or divisors) of an integer

2 is a factor of 12 because 12/2=6, which is an integer

5 is not a factor of 12 because 12/5=2.4 which is not an integer

Question 2

What can you do to determine the factors of a number?

Answer 2

Create a factor table!

Question 3

The products that result when that integer is multiplied by another integer.

Answer 3

Multiples of an integer

The multiples of 12 are:

12(1)=12, 12(2)=24, 12(3)=36…

Question 4

Multiples and factors are essentially what of each Other?

Answer 4

Opposites!

Since 6 is a factor of 24…

24 is a multiple of 6

Question 5

If an integer is divisible only by 1 and itself, then it is a

Answer 5

Prime number

2, 3, 5, 7, 11, 13, and so on!

1 is not a prime number

2 is the only even prime number

Question 6

Any factor of an integer that is also prime.

Answer 6

Prime factor

2 and 3 are prime factors of 12, but 4 is not

Question 7

Two important properties of prime factors:

Answer 7

1) any integer can be expressed as the product of its prime factors

12=223

2) the factors of any integer will be completely determined by the prime factors of that integer

12=223

The factors of 12 are 1, 2, 3, (22), (23), (223)

Question 8

The largest integer that divides evenly into all the numbers

Break the numbers down into their prime factors and circle the shared factors. The product of the scared factors is your answer

Answer 8

Greatest common factor (GCF)

Question 9

The smallest integer that is divisible by all the numbers in the set

Must contain the prime factors of each number in the set

Answer 9

Least common multiple (LCM)

Question 10

Any whole number

Answer 10

Integer

Examples: 2 and -9

3/2 and -7.2 are NOT integers

Question 11

If “a” is a factor of “b”, and “b” is a factor of “c”, then “a” must be a factor of “c”

Answer 11

If “a” is a factor of “b”, and “b” is a factor of “c”, then “a” must be a factor of “c”

Since 40 is a factor of 240, 8 and 5 (factors of 40) must also be factors of 240

Question 12

If “y” is divisible by 12, which of the following must be true?

A) “Y” is divisible by 24
B) “Y” is divisible by 6
C) “Y” is divisible by 4

Answer 12

If “y” is divisible by 12 then the prime factors of 12 must be prime factors of “y”.

Create a factor tree.

12=2^2*3

From this we know that “y” has 2,2,&3 in its prime factorization

Since “y” has 2*2 in its prime factorization, y must be divisible by 6

The correct answer is B and C

Question 13

If you are dividing, is the remainder small or larger than the number you’re dividing by?

X is an integer (quant. Comparison)

• the remainder when x is divided by 4
• 4

Answer 13

4

Because the remainder must always be smaller than the divisor