Math Lesson .6.15 - Divisibility by 15

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Welcome to our Math lesson on Divisibility by 15, this is the fifteenth 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 15

Rule: "A number is divisible by 15 if it is divisible by both 3 and 5."

For example, 3495 is divisible by 15 as it is divisible by 3 (3 + 4 + 9 + 5 = 21 ÷ 3 = 7) and also by 5 because it ends with 5.

On the other hand, 54,320 is not divisible by 15 as it is divisible by 5 (it ends with zero) but not by 3, as the sum of its digits is not divisible by 3 (5 + 4 + 3 + 2 + 0 = 14).

Likewise, 106,329 is not divisible by 15 as it is divisible by 3 (1 + 0 + 6 + 3 + 2 + 9 = 21, a number divisible by 3), but not by 5 as it does not end with 0 or 5.

Indeed, the calculator gives 3495 ÷ 15 = 233; 54,320 ÷ 15 = 3621.3333...; and 106,329 ÷ 15 = 7,088.6. These results confirm the solutions made.

Example 3

Check whether the numbers below are divisible by 11, 12, 13, 14 and 15.

1,441,440
34,471,325

Solution 3

1,441,440 is divisible by 11 because (0 + 4 + 4 + 1) - (4 + 1 + 4) = 9 - 9 = 0, which is a number divisible by 11 (zero is divisible by all numbers).
1,441,440 is divisible by 12, as it is divisible by 3 (1 + 4 + 4 + 1 + 4 + 4 + 0 = 18 ÷ 3 = 6) and also by 4 (40 ÷ 4 = 10).
1,441,440 is divisible by 13, as 440 - 441 + 1 = 0, which is divisible by 13.
1,441,440 is divisible by 14 as it is divisible both by 2 (even number) and by 7. Indeed, when we do the recurring operation (2 × last digit - the number formed by the rest of digits), we obtain 2 × 0 - 144,144 = -144,144; then 2 × 4 - 14,414 = - 14,406; then 2 × 6 - 1440 = -1428; then 2 × 8 - 142 = -126, which is a number divisible by 7 because 126 ÷ 7 = 18.
1,441,440 is divisible by 15 as it is divisible by 3 (1 + 4 + 4 + 1 + 4 + 4 + 0 = 18 ÷ 3 = 6) and also by 5 (the number ends with 5).
34,471,325 is NOT divisible by 11 as (5 + 3 + 7 + 4) - (2 + 1 + 4 + 3) = 19 - 10 = 9, which is not a number divisible by 11.
34,471,325 is NOT divisible by 12 as it is an odd number (cannot be divisible by 4)
34,471,325 is NOT divisible by 13 as 325 - 471 + 34 = -112, which is not divisible by 13.
34,471,325 is NOT divisible by 14 as it is an odd number (cannot be divisible by 2). No need to check for the divisibility by 7.
34,471,325 is NOT divisible by 15 as this number is not divisible by 3 (3 + 4 + 4 + 7 + 1 + 3 + 2 + 5 = 29, i.e. not divisible by 3) despite it being divisible by 5 (it ends with 5).

More Divisibility Rules Lessons and Learning Resources

Arithmetic Learning Material
Tutorial ID	Math Tutorial Title	Revision Notes	Revision Questions
.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 15" math lesson? People who liked the "Divisibility Rules lesson found the following resources useful:

Divide By 15 Feedback. Helps other - Leave a rating for this divide by 15 (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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