Question

Using the divisibility rules for numbers

2

and

3

, create a divisibility rule of number

6

. Use the rule to find whether the numbers

456

and

789

are divisible by

6

or not.

Accepted Answer

According to this question we need to create a divisibility rule of number $6$ using the divisibility rules for number $2$ and $3 .$ Then, we need to find whether the numbers $456$ and $789$ are divisible by $6$ or not.

Consider, a whole number " $n$ ". We know that every number can be written as the product of its prime factors.

If ’ $n$ ' is divisible by $2$ it can be written as:

$n = 2 m$ ; where $m$ is product of all other prime factors of ‘ $n$ '.

And if ’ $n$ ' is divisible by $3$ it can be written as:

$n = 3 k$ ; where $k$ is product of all other prime factors of $' n'$ .

And if ’ $n$ ’ is divisible by both $2$ and $3$ then it can be written as:

$n = 2 \times 3 \times b$ ; where $b$ is the product of other prime factors of ' $n$ '. Now, we can write:

$n = 2 \times 3 \times b = 6 \times b$

This implies that $n$ is divisible by $6$ .

We can generalize this property as :

"If a number has in its ones place either of the numbers $2, 4, 6, 8$ or $0$ and the sum of its individual digits is a multiple of $3$ , then we can say that the number is divisible by $6$ ."

Given: $456$ :

Since the number has $6$ in its ones place (it is divisible by $2$ ),

and the sum of the digits $= 4 + 5 + 6 = 15$ , which is divisible by $3$ (thus $456$ is also divisible by $3$ ),

so, we can say that $456$ is divisible by $6$

Given: $789$

As the ones place digit of the number is $9$ we can say it is not divisible by $2$ .

Therefore we can say that $789$ is not divisible by $6$ .

Using the divisibility rules for numbers $2$ and $3$ , create a divisibility rule of number $6$ . Use the rule to find whether the numbers $456$ and $789$ are divisible by $6$ or not.

Important Questions on Fundamentals of Mathematics

Learn and Prepare for any exam you want !

Using the divisibility rules for numbers 2 and 3, create a divisibility rule of number 6. Use the rule to find whether the numbers 456 and 789 are divisible by 6 or not.

Important Questions on Fundamentals of Mathematics

Learn and Prepare for any exam you want !

Using the divisibility rules for numbers $2$ and $3$ , create a divisibility rule of number $6$ . Use the rule to find whether the numbers $456$ and $789$ are divisible by $6$ or not.