Question

which of the following numbers is divisible by both 2 and 3​

Answer 1

Answer:

Since the number 4,608 is both divisible by 2 and 3 then it must also be divisible by 6. The answer is YES. A number is divisible by 9 if the sum of the digits is divisible by 9.

Answer 2

Note: the given question is incomplete as it should be as follows:

Which of the following numbers is divisible by both 3 and 2?

a) 1023    b) 4029    c) 1062    d) 2512

Solution:

Know that,

Divisibility rule for 2 states that A number is divisible by 2 if the last digit of the number is an even number.

Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

Check option (a).

Given number: $1023$.

Observe that last digit of the given number is 3, which is an odd number.

Therefore, it is not divisible by 2.

Find the sum of the given number.

$1023=1+0+2+3$

       $=6$

Observe that the sum of the given number is 6 which is divisible by 3.

Therefore, the given number is divisible by 3 but not by 2.

Hence, this is not the correct option.

Check option (b).

Given number: $4029$.

Observe that last digit of the given number is 9, which is an odd number.

Therefore, it is not divisible by 2.

Find the sum of the given number.

$4029=4+0+2+9$

       $=15$

Observe that the sum of the given number is 15 which is divisible by 3.

Therefore, the given number is divisible by 3 but not by 2.

Hence, this is not the correct option.

Check option (c).

Given number: $1062$.

Observe that last digit of the given number is 2, which is an even number.

Therefore, it is divisible by 2.

Find the sum of the given number.

$1062=1+0+6+2$

       $=9$

Observe that the sum of the given number is 9 which is divisible by 3.

Therefore, the given number is divisible by 3 and 2.

Hence, this is the correct option.

Check option (d).

Given number: $2512$.

Observe that last digit of the given number is 2, which is an even number.

Therefore, it is not divisible by 2.

Find the sum of the given number.

$2512=2+5+1+2$

       $=10$

Observe that the sum of the given number is 10 which is not divisible by 3.

Therefore, the given number is divisible by 2 but not by 3.

Hence, this is not the correct option.