The criterion of divisibility by 6 is interesting because it is analyzed using two other divisibility criteria (divisibility by 2 and divisibility by 3). This is because the number 6 is formed by multiplying 2×3, so a number divisible by 6 is that number that is divisible by 2 and 3 simultaneously.
Thus, in order to determine the criterion of divisibility by 6, we must understand the criteria of divisibility by 2 and by 3. Check out the articles “Divisibility by 2 " and "Divisibility by 3 ”
• Divisibility by 2:
"Every even number is divisible by 2"
• Divisibility by 3:
"A number divisible by 3 is one in which the sum of its digits is divisible by 3"
Therefore, we can say that the Divisibility Criterion by 6 is given as follows:
"In order for a number to be divisible by 6 it must be an even number and the sum of its digits must be divisible by 3."
Let's look at some examples where we will apply this divisibility by 6.
- Check that the following values are divisible by the number 6.
The) 192 B) 1197 ç) 4032
a) Let's check if the number 192 satisfies the conditions of divisibility by 6.
Remembering that we must check two divisibility criteria (by 2 and by 3). Since the number 192 is an even number, it satisfies the first criterion. We must now add their digits together to see if they add up to a number divisible by 3. Sum: 1 + 9 + 2=12. We know that 12 is divisible by 3, so the number 192 is also divisible by 3. As both criteria were met, we can say that 192is divisible by 6.
b) The number 1197 it is not divisible by 6 as it does not satisfy the first condition of being an even number. Note that it even satisfies the condition of being divisible by 3, however it is necessary that both conditions are met.
c) The number 4032satisfies the first condition of being an even number. Let's see if the divisibility by 3 criterion is satisfied. We must add the digits of the number 4032.
4+0+3+2=9
As 9 is divisible by 3, the second criterion was also satisfied, so we can say that the number 4032is divisible by 6.
By Gabriel Alessandro de Oliveira
Graduated in Mathematics
Kids School Team