Using divisibility tests, determine which of following numbers are
divisible by 6:
(a) 297144 (b) 1258 (c) 4335 (d) 61233
(e) 901352 (f) 438750 (g) 1790184 (h) 12583
(i) 639210 (j) 17852
Using divisibility tests, determine which of following numbers are divisible by 6:
(a) 297144 (b) 1258 (c) 4335 (d) 61233
(e) 901352 (f) 438750 (g) 1790184 (h) 12583
(i) 639210 (j) 17852
(a) 297144
Since the last digit of the number is 4, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 27. Since
27 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(b) 1258
Since the last digit of the number is 8, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 16. Since
16 is not divisible by 3, the given number is also not divisible by
3.
As the number is not divisible by both 2 and 3, it is not divisible
by 6.
(c) 4335
The last digit of the number is 5, which is not divisible by 2.
Therefore, the given number is also not divisible by 2.
On adding all the digits of the number, the sum obtained is 15. Since
15 is divisible by 3, the given number is also divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible
by 6.
(d) 61233
The last digit of the number is 3, which is not divisible by 2.
Therefore, the given number is also not divisible by 2.
On adding all the digits of the number, the sum obtained is 15. Since
15 is divisible by 3, the given number is also divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible
by 6.
(e) 901352
Since the last digit of the number is 2, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 20. Since
20 is not divisible by 3, the given number is also not divisible by
3.
As the number is not divisible by both 2 and 3, it is not divisible
by 6.
(f) 438750
Since the last digit of the number is 0, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 27. Since
27 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(g) 1790184
Since the last digit of the number is 4, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 30. Since
30 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(h) 12583
Since the last digit of the number is 3, it is not divisible by 2.
On adding all the digits of the number, the sum obtained is 19. Since
19 is not divisible by 3, the given number is also not divisible by
3.
As the number is not divisible by both 2 and 3, it is not divisible
by 6.
(i) 639210
Since the last digit of the number is 0, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 21. Since
21 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(j) 17852
Since the last digit of the number is 2, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 23. Since
23 is not divisible by 3, the given number is also not divisible by
3.
As the number is not divisible by both 2 and 3, it is not divisible
by 6.
(a) 297144
Since the last digit of the number is 4, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 27. Since 27 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(b) 1258
Since the last digit of the number is 8, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 16. Since 16 is not divisible by 3, the given number is also not divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible by 6.
(c) 4335
The last digit of the number is 5, which is not divisible by 2. Therefore, the given number is also not divisible by 2.
On adding all the digits of the number, the sum obtained is 15. Since 15 is divisible by 3, the given number is also divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible by 6.
(d) 61233
The last digit of the number is 3, which is not divisible by 2. Therefore, the given number is also not divisible by 2.
On adding all the digits of the number, the sum obtained is 15. Since 15 is divisible by 3, the given number is also divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible by 6.
(e) 901352
Since the last digit of the number is 2, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 20. Since 20 is not divisible by 3, the given number is also not divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible by 6.
(f) 438750
Since the last digit of the number is 0, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 27. Since 27 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(g) 1790184
Since the last digit of the number is 4, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 30. Since 30 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(h) 12583
Since the last digit of the number is 3, it is not divisible by 2.
On adding all the digits of the number, the sum obtained is 19. Since 19 is not divisible by 3, the given number is also not divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible by 6.
(i) 639210
Since the last digit of the number is 0, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 21. Since 21 is divisible by 3, the given number is also divisible by 3.
As the number is divisible by both 2 and 3, it is divisible by 6.
(j) 17852
Since the last digit of the number is 2, it is divisible by 2.
On adding all the digits of the number, the sum obtained is 23. Since 23 is not divisible by 3, the given number is also not divisible by 3.
As the number is not divisible by both 2 and 3, it is not divisible by 6.
