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Divisibility Rules Exploration

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Divisibility Rules Exploration

Use divisibility rules to help sort and share supplies quickly. Show how you know; a rule or calculation is enough.

Quick rules

Use these clues: divisible by 2 means the last digit is even; by 3 or 9 means the digit sum is divisible by 3 or 9; by 4 means the last two digits are divisible by 4; by 5 means the last digit is 0 or 5; by 10 means the last digit is 0. A number is divisible by 6 if it is divisible by both 2 and 3. For 8, check whether the last three digits are divisible by 8. For 11, the alternating sum of the digits must be divisible by 11.

1.The stall has 438 apples. Which divisibility clues prove that 438 can be packed equally into 2 baskets, 3 baskets, or 6 baskets? Select every correct choice.

It is even, and its digit sum is 15.
It ends in 8, so it is divisible by 5.
Its last two digits, 38, are divisible by 4.
Its digit sum is 15, so it is divisible by 9.

2.A box holds 1,260 seed packets. Fill in the missing digit sum, then name all the numbers from this list that divide 1,260 exactly: 2, 3, 4, 5, 6, 9, 10.

3.Match each test with the divisibility rule it checks. Write the correct letter beside each number: (a) last digit is 0; (b) last two digits form a multiple of 4; (c) digit sum is a multiple of 9; (d) divisible by both 2 and 3. Numbers: 4, 6, 9, 10.

Digit sum is a multiple of 9
Last two digits form a multiple of 4
Divisible by both 2 and 3
Last digit is 0

4.Two deliveries contain 2,418 jars and 3,524 jars. Which delivery can be split into equal groups of 4 without leftovers? Explain using the last-two-digits rule.

5.True or false? If a whole number is divisible by 9, it must also be divisible by 3. Give a number example to support your answer.

TrueFalse

6.A delivery code is 5□2. Which digits can go in the box to make the three-digit number divisible by 3? List all possibilities and show the digit-sum test.

7.A crate contains 23,456 apples. Use the last-three-digits rule to decide whether the apples can be shared equally among 8 stalls. Show the check.

8.A number is divisible by both 2 and 3. Is it always divisible by 6? Choose an answer and explain why this helps when checking 438.

Yes. Divisibility by both 2 and 3 means divisibility by 6.
No. It must also end in 0.
No. Its digit sum must be 9.

9.What do you notice about the multiples of 6 from 1 to 60? Explain how the divisibility rules for 2 and 3 help identify them.

10.A market worker says 1,331 is divisible by 11 because 1 − 3 + 3 − 1 = 0, and 0 is divisible by 11. Is the conclusion correct? Explain what the alternating-sum test tells you.

11.There are 84 reusable cups to arrange in equal rows, with no cups left over. List every possible whole-number row length (including 1 and 84). How many different row lengths are possible?

12.Create a four-digit stall code that is divisible by 2, 3 and 5, but not by 9. Give your code and verify each condition using divisibility rules.