Question

Which of these numbers are divisible by 6 ?
A. 12, 453
B. 23, 498
C. 56, 821
D. 78, 324

Answer 1

Hint:First we write the prime factors of 6 and then we will look at the divisibility test of all those prime factors and then we will check each of these options whether it is divisible by these prime factors or not.

Complete step-by-step answer:
As we have discussed above first we will write the prime factors of 6.
6 = $2\times 3$
Hence, 2 and 3 is the prime factor of 6.
So, now we will look at the divisibility test of 2 and 3.
Divisibility test of 2: If a number is even then it is divisible by 2.
Divisibility test of 3: If we add all the digits of a number and if it is divisible 3 then the given number is also divisible by 3.
Now we will compare each of the options one by one.
Let’s check option (a),
12 is an even number and 1+2 = 3 so, it is divisible by both 2 and 3.
453 is not even.
Hence, 12 is divisible by 6 but not 453.
So, option (a) is incorrect.

Let’s check option (b),
498 is an even number and 4+9+8 = 21 so, it is divisible by both 2 and 3.
23 is not even.
Hence, 498 is divisible by 6 but not 23.
So, option (b) is incorrect.

Let’s check option (c),
56 is an even number and 5+6 = 11 so, it is divisible by 2 but not 3.
821 is not even.
Hence, both are not divisible by 6.
So, option (c) is incorrect.

Let’s check option (d),
78 is an even number and 7+8 = 15 so, it is divisible by both 2 and 3.
324 is an even number and 3+2+4 = 9 so it is divisible by both 2 and 3.
Hence, both are divisible by 6.
So, option (d) is correct.

Note: One can also solve this question by checking each option dividing by 6 directly to point out the correct option, but it will take too much time, so go with this approach instead.Students should remember all the divisibility tests of 2,3,4,5,6,7..etc for solving these types of problems.