Prime Numbers and Divisibility

Question 1

Prime #s between 0 and 10

Answer 1

2, 3, 5 ,7

Question 2

Prime #s between 10 and 20

Answer 2

11, 13, 17, 19

Question 3

Prime #s between 20 and 30

Answer 3

23, 29

Question 4

Prime #s between 30 and 40

Answer 4

31, 37

Question 5

Prime #s between 40 and 50

Answer 5

41, 43, 47

Question 6

Prime #s between 50 and 60

Answer 6

53, 59

Question 7

Prime #s between 60 and 70

Answer 7

61, 67

Question 8

Prime #s between 70 and 80

Answer 8

71, 73, 79

Question 9

Prime #s between 80 and 90

Answer 9

83, 89

Question 10

Prime #s between 90 and 100

Answer 10

97

Question 11

Prime #s between 100 and 110

Answer 11

101, 103, 107, 109

Question 12

Divisibility by 3

Answer 12

The SUM of the integers DIGITS must be divisible by 3

Question 13

Divisibility by 4

Answer 13

The last TWO DIGITS of the number must be divisible by 4

Question 14

Divisibility by 5

Answer 14

If the integers ends in 0 or 5

Question 15

Divisibility by 6

Answer 15

Integer must be divisible by BOTH 2 and 3

Question 16

Divisibility by 8

Answer 16

The last THREE Digits of the integer must be divisible by 8 OR divisible by 2 THREE TIMES

Question 17

Divisibility by 9

Answer 17

The SUM of the integers DIGITS must be divisible by 9

Question 18

Divisibility by 10

Answer 18

the integer ends in 0

Question 19

Factor Foundation Rule: if a is divisible by ‘b’ and ‘b’ is divisible by ‘c’ -> then ‘a’ is divisible by ‘c’ as well!

Answer 19

Example: 12 is divisible by 6 and 6 is divisible by 3 –> Then 12 is also divisible by 3!

Question 20

When the GRE tells you that a number n is even –> this implies what?

Answer 20

Every even number is a multiple of 2! So n is a multiple of 2

Question 21

X is divisible by 3 and 10. Is x divisible by 45?

Answer 21

Given the information about x, we know the following prime factors: 3, 2 and 5.
Break down 45 in its prime factors: 3,3, and 5.
45 Could be a divisor but we don’t know for sure because to be sure, x must contain all the same prime factors as 45 contains!