Problem Set 33 – Multiples and Divisibility TestsClass 5 Maths · Chapter 8 Multiples and Factors · Problem Set 33 – Maharashtra Board

Summary: Problem Set 33 – Multiples and Divisibility Tests

If a number divides another with remainder 0, the bigger number is a multiple of the smaller one. The numbers in the 4 times table are multiples of 4.

To check if a number is a multiple of 7, divide it by 7. Remainder 0 means yes.

Divisible by 2: the units digit is 0, 2, 4, 6 or 8.

Divisible by 5: the units digit is 0 or 5. Divisible by 10: the units digit is 0.

In word problems, if the total is not a multiple of the piece size, find the next multiple to see how much more is needed.

Key points to remember

• Multiple = number × a whole number
• Times-table numbers are multiples
• Remainder 0 → it is a multiple
• Test for 2: units digit 0, 2, 4, 6, 8
• Test for 5: units digit 0 or 5
• Test for 10: units digit 0
• A multiple of 10 is also a multiple of 2 and 5
• Change units (m to cm, l to ml) before dividing

Problem Set 33 – Multiples and Divisibility Tests – Notes

1. What is a multiple?

• Multiples of 4 are 4, 8, 12, 16, 20… — the 4 times table.
• 48 ÷ 4 = 12, remainder 0. So 48 is a multiple of 4, and 4 is a factor of 48.
• 50 ÷ 4 leaves remainder 2, so 50 is not a multiple of 4.

2. Using multiples in daily life

• A 250 ml cup and a 2 litre bottle: 2 litres = 2000 ml. 2000 ÷ 250 = 8, remainder 0. So 8 cups fill the bottle exactly.
• Can the same cup measure 1700 ml? 1700 ÷ 250 leaves remainder 200, so no.

3. How much more is needed?

• If the total is not a multiple, find the multiple just after it.
• Then subtract to find how much more is needed.

4. Divisibility tests for 2, 5 and 10

• Look only at the units digit!
• 2: units digit 0, 2, 4, 6 or 8 (even numbers). 346 ✓, 571 ✗.
• 5: units digit 0 or 5. 735 ✓, 742 ✗.
• 10: units digit 0. 680 ✓, 685 ✗.

5. Multiples of two numbers

• A number can be a multiple of two numbers at once.
• Multiples of both 2 and 3: 6, 12, 18, 24, 30… (the 6 times table).
• Multiples of 10 are always multiples of 2 and of 5 too, since their units digit is 0.

Formulas at a glance

Key terms

Problem Set 33 – Multiples and Divisibility Tests – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 33 – Multiples and Divisibility Tests – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 33 – Multiples and Divisibility Tests

⏱ About 25 minutes

1. Learn (5 min)
   Learn what a multiple is and the tests for 2, 5 and 10.
2. Try (15 min)
   Write five 3-digit multiples each of 2, 5 and 10. Solve the ribbon and peanut problems.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.