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Number System - Factors, multiples, and primes

Grade 6IGCSE

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: Numbers in a specific number's multiplication table.

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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 prime numbers using a factor tree or division ladder.

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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.

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Divisibility Rules: Shortcuts to determine if a number is divisible by 2, 3, 5, 9, or 10.

📐Formulae

HCF=Product of common prime factors with the lowest power\text{HCF} = \text{Product of common prime factors with the lowest power}

LCM=Product of all appearing prime factors with the highest power\text{LCM} = \text{Product of all appearing prime factors with the highest power}

Relationship: a×b=HCF(a,b)×LCM(a,b)\text{Relationship: } a \times b = \text{HCF}(a, b) \times \text{LCM}(a, b)

Prime Factorization Form: n=p1a×p2b×p3c…\text{Prime Factorization Form: } n = p_1^{a} \times p_2^{b} \times p_3^{c} \dots

💡Examples

Problem 1:

Find the prime factorization of 60.

Solution:

60=22×3×560 = 2^2 \times 3 \times 5

Explanation:

Divide 60 by the smallest prime (2): 60÷2=3060 \div 2 = 30. Divide 30 by 2: 30÷2=1530 \div 2 = 15. Divide 15 by the next prime (3): 15÷3=515 \div 3 = 5. Since 5 is prime, stop. The factors are 2,2,3,52, 2, 3, 5.

Problem 2:

Find the HCF and LCM of 12 and 18.

Solution:

HCF=6,LCM=36\text{HCF} = 6, \text{LCM} = 36

Explanation:

Prime factors of 12=22×312 = 2^2 \times 3. Prime factors of 18=2×3218 = 2 \times 3^2. HCF is the lowest power of common primes: 21×31=62^1 \times 3^1 = 6. LCM is the highest power of all primes: 22×32=4×9=362^2 \times 3^2 = 4 \times 9 = 36.

Problem 3:

Identify the prime numbers between 10 and 20.

Solution:

11,13,17,1911, 13, 17, 19

Explanation:

List numbers: 11 (prime), 12 (even), 13 (prime), 14 (even), 15 (divisible by 3/5), 16 (even), 17 (prime), 18 (even), 19 (prime). Only 11, 13, 17, and 19 have no factors other than 1 and themselves.