Using divisibility tests, determine which of the 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

The prime factors of 6 are 2 and 3. So for the number to be divisible by 6, it must also be divisible by 2 and 3. Therefore, we need to check whether the number is divisible by 2 and then the sum of the digits should also be divisible by 3.

(a) 297144

Since the last digit of the number is 4, it is divisible by 2, so, the given number 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 per the divisibility rule of 6 the number is divisible by both 2 and 3, so, it is divisible by 6.

(b) 1258

Since the last digit of the number is 8, it is divisible by 2, so, the given number 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 per the divisibility rule of 6 the number should be divisible by 2 and 3 but the given number is not divisible by both 2 and 3, so, it’s not divisible by 6.

(c) 4335

Since the last digit of the number is 5, it is not divisible by 2, so, the given number is 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 per the divisibility rule of 6 the number should be divisible by both 2 and 3 the numberbut the given number is not divisible by both 2 and 3, so, it is not divisible by 6.

(d) 61233

Since the last digit of the number is 3, it is not divisible by 2, so, the given number is 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 per the divisibility rule of 6 the number should be divisible by both 2 and 3 but the given number is not divisible by both 2 and 3, so, it is not divisible by 6.

(e) 901352

Since the last digit of the number is 2, it is divisible by 2, so, the given number 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 per the divisibility rule of 6 the number should be divisible by both 2 and 3 but the given number is not divisible by both 2 and 3, so, it is not divisible by 6.

(f) 438750

Since the last digit of the number is 0, it is divisible by 2, so, the given number 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 per the divisibility rule of 6 the number should be divisible by both 2 and 3, the given number is divisible by both 2 and 3, so, it is divisible by 6.

(g) 1790184

Since the last digit of the number is 4, it is divisible by 2, so, the given number is divisible by 2

On adding all the digits number the sum obtained is 30 since 30 is divisible by 3, the given number is also divisible by 3.

As per the divisibility rule of 6 the number should be divisible by both 2 and 3 and the given number is divisible by both 2 and 3, so, it is divisible by 6.

(h) 12583

Since the last digit of the number is 3, it is divisible by 2, so, the given number is not divisible by 2

On adding all the digits number the sum obtained is 19 since 19 is not divisible by 3, the given number is also not divisible by 3.

As per the divisibility rule of 6 the number should be divisible by both 2 and 3 but the given number is not divisible by both 2 and 3, so, it is not divisible by 6.

(i) 639210

Since the last digit of the number is 0, it is divisible by 2, so, the given number is divisible by 2

On adding all the digits number the sum obtained is 21 since 21 is divisible by 3, the given number is also divisible by 3.

As per the divisibility rule of 6 the number should be divisible by both 2 & 3 and the given number is divisible by both 2 and 3, so, it is divisible by 6.

(j) 17852

Since the last digit of the number is 2, it is divisible by 2, so, the given number is divisible by 2

On adding all the digits number the sum obtained is 23, since 23 is not divisible by 3, the given number is also not divisible by 3.

As per the divisibility rule of 6 the number should be divisible by both 2 and 3 but the given number is not divisible by both 2 and 3, so, it is not divisible by 6.