Problems Involving Divisibility Rules - easy

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)

Solution:
The numbers which end with (0, 2, 4, 6, 8) are divisible by 2.
38536 ends with "6", hence it is divisible by 2.

Solution:
The number whose last 2 digits are separately divisible by 4 is also wholly divisible by 4.
19232 ends with "32" which is divisible by 4. Hence 19232 is divisible by 4.

Solution:
The numbers that end with 0 are divisible by 10.
59627 ends with "7" therefore it is not divisible by 10.

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.

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.

Solution:
The number whose last 2 digits are separately divisible by 4, is wholly divisible by 4.
86422 ends with "22", which is not divisible by 4.
95421 ends with "21", which is not divisible by 4.
43216 ends with "16", which is divisible by 4. Hence 43216 is divisible by 4.

Solution:
The numbers that end with 5 or 0 are divisible by 5.
2417 ends with "7", hence it is not divisible by 5.
9315 ends with "5", hence it IS divisible by 5.
3142 ends with "2", hence it is not divisible by 5.

Solution:
The numbers which end with (0, 2, 4, 6, 8) are divisible by 2.
95321 ends with "1", hence it is NOT divisible by 2.
15632 ends with "2", hence it IS divisible by 2.
85617 ends with "7", hence it is NOT divisible by 2.

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.

Solution:
The number 8561 is odd because it ends with "1". The numbers that end in (0, 2, 4, 6, 8) are divisible by 2, and henceforth even. Therefore 8561 is an odd number.

Solution:
The number 68563 is odd because it ends with "3". The numbers that end in (0, 2, 4, 6, 8) are divisible by 2, and henceforth even. Therefore 68563 is an odd number.

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)

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 with "2", hence it is divisible by 2. But (3+9+0+5+2) = 19, which is not divisible by 3.
80148 ends with "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 with "5", hence it is NOT divisible by 2. But (5+2+3+3+5) = 18, which is divisible by 3.