DIVISIBILITY RULES WORKSHEET

Divisibility rule for 2

Problem 1 :

Which of these numbers are divisible by 2?

a) 216     b) 3184     c) 827    d) 4770   e) 123 456

Solution

Problem 2 :

If a and b are odd numbers, then which of the following is even ?

a) a + b    b) a + b + 1    c) ab    d) ab + 2

Solution

Problem 3 :

n is a whole number when divided by 4 gives 3 as remainder What will be the remainder when 2n is divided by 4.

a) 3    b)  2      c) 1      d) 0

Solution

Problem 4 :

A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is

a) 214   b)  476    c)  954   d)  1908

Solution

Problem 5 :

Which number is divisible by 2?

75, 45, 46, 49

a. 75      b. 45      c. 49     d. 46

Problem 6 :

Which number is divisible by 4?

34, 51, 68, 38

a. 68      b. 34      c. 51     d. 38

Solution

Problem 7 :

Which number is divisible by 2 but not by 4?

92, 115, 138, 184

a. 184      b. 138       c. 92      d. 115

Solution

Problem 8 :

Which number is divisible by 9?

324 581, 324 664, 324 747, 324 867

a. 324 664      b. 324 867     c. 324 581     d. 324 747

Solution

Problem 9 :

Which number is divisible by 3 and by 5?

378, 380, 375, 385

a. 378      b. 385      c. 380        d. 375

Solution

Problem 10 :

Use the divisibility rules to find all the factors of 102.

a. 2, 3, 6, 17, 34, 51                  b. 1, 2, 3, 6, 17, 102

c. 1, 2, 3, 6, 17, 34, 51, 102             d. 1, 2, 3, 102

Solution

Divisibility rule for 3

Problem 1 :

Which of these numbers are divisible by 3?

a) 84   b) 123  c) 437  d) 111114  e) 707052

Solution

Problem 2 :

If the number 517__324 is completely divisibly by 3, then the smallest whole number is the place of ___ will be 

a) 0   b)   1     c)  2      d) none

Solution

Problem 3 :

How many 3 digit numbers are divisible by 3.

Solution

Problem 4 :

What digits could replace ___so that these numbers are divisible by 3?

a) 3_8      b)  8__5     c)  3__14     d) __229

Solution

Problem 5 :

If the seven digit number 52A6B7C is divisible by 33, and A, B and C are primes then the maximum value of 2A + 3B + C is

a)  32    b) 23    c)  27   d) 34

Solution

Divisibility rule for 4

Problem 1 :

Which of these numbers are divisible by 4?

a) 482   b) 2556  c) 8762  d) 12368  e) 213 186

Solution

Problem 2 :

If the product of 4864 x 9P2 is divisible by 12, the value of P is 

a)  1     b)  5    c) 6      d) 8

Solution

Problem 3 :

Consider the numbers of the form 3__8. Which digits could be put in place of ___.So that the number 3___8 is :

a) even  b) divisible by 3  c) divisible by 4

Solution

Problem 4 :

There are 360 minutes of monthly cell phone minutes for 4 people in a family. Can each person get the same number of minutes per month? If so, how many?

Solution

Problem 5 :

Assume that there are 365 days in a year. Describe the possible number of days in a week so that there is an exact number of weeks in a year.

Solution

Problem 6 :

A shopkeeper packs pencils in boxes of 6. He has 5784 pencils. Will he be able to pack them all without leaving any pencil ? Show how you decide.

Solution

Problem 7 :

A teacher writes the number 145431 on the board and asks if it is divisible by 11. Help the class decide, showing each step clearly.

Solution

Divisibility rule for 5

Problem 1 :

Which of these numbers are divisible by 5?

a) 400    b) 628    c) 735    d) 21063    e) 384 005

Solution

Problem 2 :

Which one of the following numbers is completely divisible by 45 ?

a)  181560    b) 331145     c)  202860      d) 2033550

Solution

Problem 3 :

The sum of all two digit numbers divisible by 5 ?

a) 1035   b) 1245   c) 1230    d) 945

Solution

Problem 4 :

What is the least number that could replace to make the number 36__5 divisible by 9?

a. 14       b. 5       c. 9       d. 4

Solution

Problem 5 :

What is the least digit you would add to 44658 to make the number divisible by 5?

Solution

Problem 6 :

Copy the diagram.

Place the numbers in the Venn diagram. 33, 12, 20, 14, 27, 18, 26, 39 Which numbers were placed in the overlapping region?

Solution

Problem 7 :

How many numbers are there from 400 to 700 which are divisible by 5, 6 and 7 ?

a) 5     b)  20    c) 2    d) 10

Solution

Problem 8 :

How many numbers are from 300 to 650 which are divisible by both 5 and 7 ?

a) 8   b)  9    c)  10    d)  12

Solution

Problem 9 :

How many numbers are there between 1 and 200 which are divisible by 3 but not 7 ?

a) 38   b)  45   c) 57    d)  66

Solution

Divisibility rule for 6

Problem 1 :

Which of these numbers are divisible by 6?

a) 162   b) 381  c) 1602  d) 2156  e) 5364

Solution

Problem 2 :

What smallest number should be added to 4456 so that sum of the number is completely divisible by 6 ?

a) 4    b)  3    c)  2    d)   1

Solution

Problem 3 :

Paul believes that the number forms alongside are always divisible by 6 :

a) Check that the first four of them are divisible by 6.

(i)  2³ – 1³ – 1

(ii)  3³ – 2³ – 1

(iii)  4³ – 3³ – 1

(iv)  5³ – 4³ – 1

b) Check that 10³ – 9³ – 1 is divisible by 6.

Solution

Problem 4 :

There are 9 students in your class. Can you divide 839 stamps evenly, so that each student in your class gets the same number of stamps?

Solution

Problem 5 :

3⁵⁰ + 9²⁶ + 27¹⁸ + 9²⁸ + 9²⁹ is divisible by which of the following integers ?

a) 11    b)  5     c) 7     d) 2

Solution