Number Theory

Which of the following are factors of 42.

• 3

• 4

• 7

• 14

• 21

Answer explanation

42 can be divided exactly by 1, 2, 3, 6, 7,14, 21 and 42.

Tags

CCSS.4.OA.B.4

Tick all multiples of 8.

• 4

• 8

• 20

• 28

• 56

Answer explanation

8 can be divided exactly by itself.

Also, 56 can be divided exactly by 8.

Tags

CCSS.4.OA.B.4

Tick the TRUE statement/s.

• odd + odd = odd

• even - odd = even

• odd x even = even

Answer explanation

ex.

3 (odd) x 4 (even) = 12 (even)

Tags

CCSS.3.OA.D.9

What are the missing prime numbers in the sequence?

2, 3, 5, 7, _____, 13, ______,19, 23

(a)  

Answer explanation

Prime numbers can only be divided evenly by the number 1 and itself. They only have 2 factors.

11 = 11 x 1

17 = 17 x 1

Tags

CCSS.4.OA.B.4

Which is a common multiple of 3 and 4?

• 7

• 9

• 12

• 16

Answer explanation

Multiples of 3 - 3, 6, 9, 12

Multiples of 4 - 4, 8, 12

Common multiple: 12...

12 can be divided exactly by 3.

Also, 12 can be divided exactly by 4.

Which is a common factor of 20 and 30?

• 3

• 4

• 5

• 6

Answer explanation

20 - 1,2,4,5,10,20

30 - 1,2,3,5,6,10,15,30

20 can be divided exactly 5.

Also, 30 can be divided exactly by 5.

Which of the following is divisible by 2, 5 and 4?

• 149

• 19 400

• 720 345

• 125 370

Answer explanation

Rule:

Divisible by 2 - the number should be even

Divisible by 5 - the number ends in 5 or 0

Divisible by 4 - the number ends in 00 or a number that can be divided exactly by 4.

19400 ...

is even

ends in 0

ends in 00

Tags

CCSS.4.OA.B.4

These are square numbers. What are the next two numbers in the sequence?

1, 4, 9, 16, 25 , _____, ______.

(a)  

Answer explanation

Square numbers are the product when a number is multiplied by itself.

$6^2$ = 6 x 6 = 36
$7^2$ = 7 x 7 = 49

Tags

CCSS.4.OA.C.5

What is the 6th number in the pattern of triangular numbers?

• 5

• 18

• 21

• 28

Answer explanation

Triangular numbers is a series of numbers obtained by continued addition of counting numbers 1, 2, 3, 4, 5, etc.

Formula

Tn = n (n + 1)/2

1st: 1

2nd: 1 + 2 = 3

3rd: 1 + 2 + 3 = 6

4th: 1 + 2 + 3 + 4 = 10

5th: 1 + 2 + 3 + 4 + 5 = 15

6th: 1 + 2 + 3 + 4 + 5 + 6 = 21

T6 = (6 x 7)/2 = 21

Tags

CCSS.4.OA.C.5

Which same number will make the calculation correct?

_____ x _____ = 144

(a)  

Answer explanation

12 x 12 = 144
$12^2$ = 144

$\sqrt{144}$ = 12, 12 is the square root of 144.

Tags

CCSS.4.OA.B.4