Problem Set 32 – Factors of a NumberClass 5 Maths · Chapter 8 Multiples and Factors · Problem Set 32 – Maharashtra Board

Summary: Problem Set 32 – Factors of a Number

When a number can be divided by another number with remainder 0, the second number is a factor (or divisor) of the first.

Factors tell us the equal group sizes we can make with nothing left over: 18 can be grouped in 1s, 2s, 3s, 6s, 9s or 18s.

1 is a factor of every number, and every number is a factor of itself.

Find factors in pairs that multiply to the number: 18 = 1 × 18 = 2 × 9 = 3 × 6. So the factors are 1, 2, 3, 6, 9, 18.

If 4 is a factor of 28, then 28 is a multiple of 4, because 28 = 4 × 7.

Key points to remember

• Factor = divides exactly, remainder 0
• Factor and divisor mean the same here
• 1 is a factor of every number
• A number is a factor of itself
• Find factors in multiplying pairs
• Stop when the pairs start to repeat
• A factor is never bigger than the number
• If a is a factor of b, then b is a multiple of a

Problem Set 32 – Factors of a Number – Notes

1. Equal groups, none left over

• Suppose you have 18 sweets and want equal groups with no sweet left.
• 18 ÷ 2 = 9, remainder 0 → groups of 2 work. 18 ÷ 4 = 4, remainder 2 → groups of 4 do not work.
• Every group size that works is a factor of 18.

2. What is a factor?

• If a number divides another number exactly (remainder 0), it is a factor or divisor of that number.
• 5 is a factor of 15 because 15 ÷ 5 = 3, remainder 0.
• 5 is not a factor of 17 because 17 ÷ 5 leaves remainder 2.

3. Finding all factors in pairs

• Start with 1 × the number. Then try 2, 3, 4… in turn.
• Each time the division is exact, write down both numbers of the pair.
• Stop when the next number to try is already in your list.

4. Numbers with few factors

• Some numbers have only two factors: 1 and the number itself. Factors of 7: 1, 7. Factors of 13: 1, 13.
• Some numbers have a factor pair with the same number twice: 25 = 5 × 5. Write 5 only once: 1, 5, 25.
• Factors of 32: 1, 2, 4, 8, 16, 32.

5. Factors and multiples

• If the division leaves no remainder, the number being divided (the dividend) is a multiple of the divisor.
• 30 ÷ 6 = 5, remainder 0. So 6 is a factor of 30 and 30 is a multiple of 6.
• The multiple is the product of the divisor and the quotient: 30 = 6 × 5.

Formulas at a glance

Key terms

Problem Set 32 – Factors of a Number – Flashcards

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

Problem Set 32 – Factors of a Number – MCQ Quiz

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

How to study Problem Set 32 – Factors of a Number

⏱ About 20 minutes

1. Learn (5 min)
   Learn what a factor is and the pair method.
2. Find (10 min)
   Find the factors of 8, 5, 14, 10, 7, 22, 25, 32 and 33 using pairs.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.