krit.club logo

Calculations - Multiples, factors, and prime numbers

Grade 4IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Multiples: These are numbers you get when you multiply a number by other whole numbers (the 'times table' of a number).

•

Factors: These are whole numbers that divide exactly into another number without leaving a remainder.

•

Factor Pairs: Two numbers that, when multiplied together, give a specific product.

•

Prime Numbers: A number greater than 1 that has exactly two factors: 1 and itself.

•

Composite Numbers: A number that has more than two factors (most whole numbers that are not prime).

•

The Number 1: A special case that is neither prime nor composite because it only has one factor (itself).

📐Formulae

Multiple=Number×n\text{Multiple} = \text{Number} \times n (where nn is any whole number 1,2,3...1, 2, 3...)

Dividend÷Factor=Whole Number quotient (no remainder)\text{Dividend} \div \text{Factor} = \text{Whole Number quotient (no remainder)}

Factor A×Factor B=Product\text{Factor A} \times \text{Factor B} = \text{Product}

💡Examples

Problem 1:

List the first five multiples of 7.

Solution:

7, 14, 21, 28, 35

Explanation:

Multiples are found by skip-counting or multiplying: 7×1=77 \times 1 = 7, 7×2=147 \times 2 = 14, 7×3=217 \times 3 = 21, 7×4=287 \times 4 = 28, and 7×5=357 \times 5 = 35.

Problem 2:

Find all the factors of 12.

Solution:

1, 2, 3, 4, 6, 12

Explanation:

We look for factor pairs that multiply to 12: 1×121 \times 12, 2×62 \times 6, and 3×43 \times 4. Listing them in order gives 1, 2, 3, 4, 6, and 12.

Problem 3:

Is 15 a prime number or a composite number? Explain why.

Solution:

Composite

Explanation:

A prime number has only two factors (1 and itself). The factors of 15 are 1, 3, 5, and 15. Since it has more than two factors, it is composite.

Problem 4:

Identify all prime numbers between 10 and 20.

Solution:

11, 13, 17, 19

Explanation:

Check each number: 11 (factors: 1, 11), 12 (even, so 2 is a factor), 13 (factors: 1, 13), 14 (even), 15 (ends in 5, so 5 is a factor), 16 (even), 17 (factors: 1, 17), 18 (even), 19 (factors: 1, 19).