Number Properties Rules

Question 0

Integer divisibility

/ by 3 if

Answer 0

It’s digits add up to a multiple of 3:

516 => 5+1+6=12 => 12/3=4

Question 1

Integer divisibility

/ By 2 if

Answer 1

The integer is even

Question 2

Integer divisibility

/ by 4 if

Answer 2

It’s last 2 digits are divisible by 4

54824 => 24/4=6

Question 3

Integer divisibility

/ by 5 if

Answer 3

It’s last digit is 5 or 0

10, 50, 1050, 28740

Question 4

Integer divisibility

/ by 6 if

Answer 4

It is a multiple of 2 and 3

558 is even => multiple of 2

5+5+8=18 => 18/3=6 => multiple of 3

Question 5

Integer divisibility

/ by 8 if

Answer 5

It’s last 3 digits are a multiple of 8

17336 => 336/8=42 => divisible by 8

Question 6

Integer divisibility

/ by 9 if

Answer 6

Digits add to a multiple of 9

6417 => 6+4+1+7=18

18/9=2 => 6417 is divisible by 9

Question 7

Integer divisibility

/ by 10 if

Answer 7

It ends in 0

100, 1790, 12460

Question 8

Integer divisibility

/ by 12 if

Answer 8

Multiple of 3 and 4

Question 9

Least common multiple

1) Do a factor tree
18=2^13^2
24=2^33^1

LCM=2^33^2=89=72

Answer 9

Do it

Question 10

Negative exponents

2^-4

X^-1

X^-2

Answer 10

Positive reciprocal

1/2^4=1/16

1/X

1/X^2

Question 11

Exponent combinations:

X^2Y^3=xxyy*y

n^53^-4=(nnnnn)/(3333)

Answer 11

Do it

Question 12

Exponent multiplication:

(2^3)(2^2)=

Answer 12

Add the exponents

=(222)(2*2)=2^5

Question 13

Exponent division with same base

4^9/4^4=

Answer 13

Subtract exponents

4^(9-4)=4^5

Question 14

(a^6b^3)/(a^2b)=

Answer 14

=(a^6/a^2)(b^3/b)=(a^6-2)(b^3-1)

=a^4*b^2

Question 15

Raising an exponent to an exponent

(x^3)^5=

Answer 15

Multiply the exponents

=x^(3*5)=x^15

Question 16

Raising a product in parentheses to a power

(X^2*Y^4)^3=

Answer 16

Distribute throughout entire parentheses

=X^(23)Y^(43)=X^6Y^12