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

We know that,
Divisibility by 6: A number is also divisible by 6 if it can be divided by 2 and 3 together.

(a) 297144
Since the number's final digit is 4, The number can therefore be divided by two.
The total of the number's digits equals 27, which may be divided into three parts. The number is therefore divisible by 3.
The number can be divided by both 2 and 3. Therefore, the number can be divided by 6.

(b) 1258
Since 8 is the number's last digit, The number can therefore be divided by two.
The total of the number's digits is 16, which cannot be divided by three. The number is therefore not divisible by three.
The number cannot be divided by both 2 and 3. Therefore, the number cannot be divided by 6.

(c) 4335
Since the number's final digit, 5, is not divisible by two, the answer is 10. The number is therefore not divisible by two.
The total of the number's digits equals 15, which can be divided into three parts. The number is therefore divisible by 3
The number cannot be divided by both 2 and 3. Therefore, the number cannot be divided by 6.

(d) 61233
Since the number's last digit is 3, which cannot be divided by 2, the answer is 10. The number is therefore not divisible by two.
The total of the number's digits equals 15, which can be divided into three parts. The number is therefore divisible by 3.
The number cannot be divided by both 2 and 3. Therefore, the number cannot be divided by 6.

(e) 901352
Since the number's last digit is 2, The number can therefore be divided by two.
The total of the number's digits is 20, which cannot be divided by 3. The number is therefore not divisible by three.
The number cannot be divided by both 2 and 3. Therefore, the number cannot be divided by 6.

(f) 438750

Considering that the number's last digit is 0, The number can therefore be divided by two.

The total of the number's digits equals 27, which may be divided into three parts. The number is therefore divisible by 3.

The number can be divided by both 2 and 3. Therefore, the number can be divided by 6.

(g) 1790184

Since the number's final digit is 4, The number can therefore be divided by two.

The total of the number's digits equals 30, which can be divided into three parts. The number is therefore divisible by 3.

The number can be divided by both 2 and 3. Therefore, the number can be divided by 6.

(h) 12583
Since the number's last digit is 3, The number is therefore not divisible by two.
The total of the number's digits is 19, which cannot be divided by 3. The number is therefore not divisible by three.
The number cannot be divided by both 2 and 3. Therefore, the number cannot be divided by 6.

(i) 639210
Considering that the number's last digit is 0, The number can therefore be divided by two.
The total of the number's digits gives us 21, which may be divided into three parts. The number is therefore divisible by 3.
The number can be divided by both 2 and 3. Therefore, the number can be divided by 6.

(j) 17852
Since the number's last digit is 2, The number can therefore be divided by two.
The total of the number's digits is 23, which cannot be divided by 3. The number is therefore not divisible by three.
The number cannot be divided by both 2 and 3. Therefore, the number cannot be divided by 6.