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Easy
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Problems Involving Divisibility Rules: Problems with Solutions
Problems involving divisibility rules by 2, 3, 4, 5, 9.
Problem 1
Which of the following numbers is even?
3643
5318
8517
Solution:
The number 5318 is even because it is divisible by 2(all numbers with last digit 0, 2, 4, 6, 8 are divisible by 2)
Problem 2
Which of the following numbers is even?
51789
18565
82628
Solution:
The number 82628 is even because it is divisible by 2(all numbers with last digit 0, 2, 4, 6, 8 are divisible by 2)
Problem 3
Which of the following numbers is odd?
68563
92162
28954
Solution:
The number 68563 is odd because it ends in "3". The numbers that end in (0, 2, 4, 6, 8) are divisible by 2, and henceforth even. Therefore 68563 is an odd number.
Problem 4
Which of the following numbers is odd?
2154
8561
1806
Solution:
The number 8561 is odd because it ends in 1. The numbers that end in (0, 2, 4, 6, 8) are divisible by 2, and henceforth even. Therefore 8561 is an odd number.
Problem 5
Which of the following numbers is divisible by 3?
51412
86221
63693
Solution:
For, 51412 (5+1+4+1+2) = 13, which is NOT divisible by 3. Hence 51412 is not divisible by 3.
For, 86221 (8+6+2+2+1) = 19, which is NOT divisible by 3. Hence 86221 is not divisible by 3.
For, 63693 (6+3+6+9+3) = 27, which IS divisible by 3. Hence 63693 is divisible by 3.
Problem 6
Which of the following numbers is divisible by 2?
95321
15632
85617
Solution:
The numbers which end with (0, 2, 4, 6, 8) are divisible by 2.
95321 ends in 1, hence it is NOT divisible by 2.
15632 ends in 2, hence it IS divisible by 2.
85617 ends in 7, hence it is NOT divisible by 2.
Problem 7
Which of the following numbers is divisible by 5?
2417
9315
3142
Solution:
The numbers that end with 5 or 0 are divisible by 5.
2417 ends in "7", hence it is not divisible by 5.
9315 ends in "5", hence it IS divisible by 5.
3142 ends in "2", hence it is not divisible by 5.
Problem 8
Which of the following numbers is divisible by 4?
86422
95421
43216
Solution:
The number whose last 2 digits are separately divisible by 4, is wholly divisible by 4.
86422 ends in "22", which is not divisible by 4.
95421 ends in "21", which is not divisible by 4.
43216 ends in "16", which is divisible by 4. Hence 43216 is divisible by 4.
Problem 9
Which of the following numbers is divisible by 9?
6821
1962
9633
Solution:
The number for which the sum of all individual digits is divisible by 9, is wholly divisible by 9.
For 6821, (6+8+2+1) = 17, which is NOT divisible by 9.
For 1962, (1+9+6+2) = 18, which is divisible by 9. Therefore 1962 is divisible by 9.
For 9633, (9+6+3+3) = 21, which is NOT divisible by 9.
Problem 10
Is 19537 divisible by 3?
Solution:
The number for which the sum of all individual digits is divisible by 3, is wholly divisible by 3.
1+9+5+3+7 = 25, which is NOT divisible by 3. Hence 19537 is not divisible by 3.
Problem 11
Is 59627 divisible by 10?
Solution:
The numbers that end with 0 are divisible by 10.
59627 ends in 7 therefore it is not divisible by 10.
Problem 12
Is 19232 divisible by 4?
Solution:
The number whose last 2 digits are separately divisible by 4 is also wholly divisible by 4.
19232 ends in 32 which is divisible by 4. Hence 19232 is divisible by 4.
Problem 13
Is 38536 divisible by 2?
Solution:
The numbers which end with (0, 2, 4, 6, 8) are divisible by 2.
38536 ends in 6, hence it is divisible by 2.
Problem 14
Which of the following numbers is divisible by 6?
39052
80148
52335
Solution:
The numbers which are divisible by both 3 and 2 are also divisible by 6. The numbers which end with (0, 2, 4, 6, 8) are divisible by 2, and the numbers for which the sum of all individual digits is divisible by 3 is wholly divisible by 3.
39052 ends in 2, hence it is divisible by 2. But (3+9+0+5+2) = 19, which is not divisible by 3.
80148 ends in 8, hence it is divisible by 2. And (8+0+1+4+8) = 21, which is divisible by 3. Therefore it is divisible by 6.
52335 ends in 5, hence it is NOT divisible by 2. But (5+2+3+3+5) = 18, which is divisible by 3.
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