Number System - Prime numbers, factors, and multiples

Grade 5IGCSE

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

🔑Concepts

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Factors: Numbers that divide exactly into another number without leaving a remainder.

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Multiples: The product of a given number and any whole number (the 'times table' of a number).

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Prime Numbers: Numbers greater than 1 that have exactly two factors: 1 and themselves (e.g., 2, 3, 5, 7, 11).

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Composite Numbers: Numbers that have more than two factors.

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Prime Factorization: Breaking down a composite number into a product of its prime factors using a factor tree.

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Highest Common Factor (HCF): The largest factor shared by two or more numbers.

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Lowest Common Multiple (LCM): The smallest multiple shared by two or more numbers.

📐Formulae

Factor \times Factor = Product

Prime \ Number \implies \text{Number of factors} = 2

LCM(a, b) = \text{The smallest value in } \{multiples \ of \ a\} \cap \{multiples \ of \ b\}

HCF(a, b) = \text{The largest value in } \{factors \ of \ a\} \cap \{factors \ of \ b\}

💡Examples

Problem 1:

Find all the factors of 20.

Solution:

1, 2, 4, 5, 10, 20

Explanation:

To find factors, look for pairs that multiply to 20: 1x20, 2x10, 4x5. Listing them in order gives the complete set.

Problem 2:

Express 12 as a product of prime factors.

Solution:

2 \times 2 \times 3

Explanation:

Divide 12 by the smallest prime (2) to get 6. Divide 6 by 2 to get 3. Since 3 is prime, the process stops. The prime factors are 2, 2, and 3.

Problem 3:

Find the HCF and LCM of 6 and 8.

Solution:

HCF = 2, LCM = 24

Explanation:

Factors of 6: {1, 2, 3, 6}. Factors of 8: {1, 2, 4, 8}. The largest shared factor is 2. Multiples of 6: {6, 12, 18, 24, 30...}. Multiples of 8: {8, 16, 24, 32...}. The smallest shared multiple is 24.

Problem 4:

Which of the following numbers are prime: 1, 2, 9, 15, 17?

Solution:

2 and 17

Explanation:

1 is not prime (it only has one factor). 9 is composite (1, 3, 9). 15 is composite (1, 3, 5, 15). 2 and 17 only have 1 and themselves as factors.