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Mathnasium #MathTricks: Divisibility (Rule for 6’s)

Jan 22, 2024

Welcome to Mathnasium’s Math Tricks series. Today we are determining whether a number is divisible by 6.

A composite number is a number that has three or more distinct factors: 1, itself, and at least one other number. We can determine whether any number is divisible by a composite number by determining whether that number is divisible by a pair of the composite number’s factors.

In this case, 6 is a composite number because its factors are: 1, 2, 3, 6. Therefore, a number is divisible by 6 if …

it is divisible by 2 AND it is divisible by 3.

Follow the examples below to determine whether the numbers are divisible by 6.

Example 1: Is 236 divisible by 6?

Step 1: Determine if the number is divisible by 2.
A number is divisible by 2 if it is even. We can quickly tell that 236 is an even number because its ones digit, 6, is even. So, 236 is divisible by 2.

If 236 weren’t divisible by 2, then we could stop there and determine that 236 also wasn’t divisible by 6. Because it is divisible by 2, we can move on to the next step.

Step 2: Determine if the number is also divisible by 3.
A number is divisible by 3 if the sum of its digits is also divisible by 3. The sum of the digits of 236 is

2 + 3 + 6 = 11.

Since 11 is not divisible by 3, then 236 is not divisible by 3.

Answer: No. Since 236 is not divisible by 2 and 3, it is not divisible by 6.

Example 2: Is 1,512 divisible by 6?

Step 1: Determine if the number is divisible by 2.
A number is divisible by 2 if it is even. We can quickly tell that 1,512 is an even number because its ones digit, 2, is even. So, 1,512 is divisible by 2.

If 1,512 weren’t divisible by 2, then we could stop there and determine that 1,512 also wasn’t divisible by 6. Because it is divisible by 2, we can move on to the next step.

Step 2: Determine if the number is also divisible by 3.
A number is divisible by 3 if the sum of its digits is also divisible by 3. The sum of the digits of 1,512 is

1 + 5 + 1 + 2 = 9.

Since 9 is divisible by 3, then 1,512 is divisible by 3.

Answer: Yes. Since 1,512 is divisible by 2 and 3, it is divisible by 6.

Now, with this strategy, you are ready to use this Mathnasium Math Trick to determine if a number is divisible by 6. Click here for more practice problems, then check your answers here.

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