Math Lesson 1.6.6 - Divisibility by 6

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Welcome to our Math lesson on Divisibility by 6, this is the sixth lesson of our suite of math lessons covering the topic of Divisibility Rules, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Divisibility by 6

Rule: "A number is divisible by 6 if it is divisible by both 2 and 3."

For example, the number 258 is divisible by 6 as it is divisible by 2 (even number) and also by 3 [the sum of digits forms a number divisible by 3, i.e. 2 + 5 + 8 = 15 ÷ 3 = 5 (0)].

On the other hand, 158 is divisible by 2 (even number) but not by 3 (the sum of digits not divisible by 3 because 1 + 5 + 8 = 14 and this number is not divisible by 3). This means 158 is not divisible by 6.

Likewise, 357 is divisible by 3 (the sum of digits divisible by 3, i.e. 3 + 5 + 7 = 15, which is a number divisible by 3), but not by 2 (odd number).

When we check the results using a calculator, we obtain 258 ÷ 6 = 43, 158 ÷ 6 = 26.333... and 357 ÷ 6 = 59.5, results that confirm the findings obtained using the divisibility rules.

Example 1

Check whether the following numbers are divisible by 2, 3, 4, 5 and 6 or not.

37,917
219,072
3,441,080

Solution 1

37,917 is NOT divisible by 2 as it is an odd number.
37,917 is divisible by 3 as 3 + 7 + 9 + 1 + 7 = 27 ⁝ 3.
37,917 is NOT divisible by 4 as the number 17 formed by its last two digits is not divisible by 4.
37,917 is NOT divisible by 5, as its last digit is neither 0 nor 5 but 7 instead.
37,917 is NOT divisible by 6 as it is divisible by 3 but not by 2 as found above.
219072 is divisible by 2 as it is an even number.
219072 is divisible by 3 as the sum of its digits is divisible by 3 (2 + 1 + 9 + 0 + 7 + 2 = 21 ⁝ 3).
219,072 is divisible by 4 as the last two digits (72) form a number divisible by 4 (72 ÷ 4 = 18).
219072 is NOT divisible by 5, as this number does not end with 0 or 5.
219072 is divisible by 6 as it is divisible by both 2 and 3 as found above.
3,441,080 is divisible by 2 as it is an even number.
3,441,080 is NOT divisible by 3 as the sum of its digits is not divisible by 3 (3 + 4 + 4 + 1 + 0 + 8 + 0 = 20, which is not divisible by 3).
3,441,080 is divisible by 4 as the number 80 formed by its last two digits is divisible by 4 (80 ÷ 4 = 20).
3,441,080 is divisible by 5 as it ends with 0.
3,441,080 is NOT divisible by 6 as it is not divisible by 3.

More Divisibility Rules Lessons and Learning Resources

Arithmetic Learning Material
Tutorial ID	Math Tutorial Title	Revision Notes	Revision Questions
1.6	Divisibility Rules
Lesson ID	Math Lesson Title	Lesson	Video Lesson
1.6.1	Divisibility by 1
1.6.2	Divisibility by 2
1.6.3	Divisibility by 3
1.6.4	Divisibility by 4
1.6.5	Divisibility by 5
1.6.6	Divisibility by 6
1.6.7	Divisibility by 7
1.6.8	Divisibility by 8
1.6.9	Divisibility by 9
1.6.10	Divisibility by 10
1.6.11	Divisibility by 11
1.6.12	Divisibility by 12
1.6.13	Divisibility by 13
1.6.14	Divisibility by 14
1.6.15	Divisibility by 15
1.6.16	Divisibility by 16
1.6.17	Divisibility by 17
1.6.18	Divisibility by 18
1.6.19	Divisibility by 19
1.6.20	Divisibility by 20
1.6.21	Other Divisibility Rules. How Relatively Prime Numbers Determine the Divisibility Rules.

Whats next?

Enjoy the "Divisibility by 6" math lesson? People who liked the "Divisibility Rules lesson found the following resources useful:

Divide By 6 Feedback. Helps other - Leave a rating for this divide by 6 (see below)
Arithmetic Math tutorial: Divisibility Rules. Read the Divisibility Rules math tutorial and build your math knowledge of Arithmetic
Arithmetic Video tutorial: Divisibility Rules. Watch or listen to the Divisibility Rules video tutorial, a useful way to help you revise when travelling to and from school/college
Arithmetic Revision Notes: Divisibility Rules. Print the notes so you can revise the key points covered in the math tutorial for Divisibility Rules
Arithmetic Practice Questions: Divisibility Rules. Test and improve your knowledge of Divisibility Rules with example questins and answers
Check your calculations for Arithmetic questions with our excellent Arithmetic calculators which contain full equations and calculations clearly displayed line by line. See the Arithmetic Calculators by iCalculator™ below.
Continuing learning arithmetic - read our next math tutorial: Decimal Number System and Other Numbering Systems

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