AQA · Mathematics · 8300
GCSE Maths: Number: product of primes
Number · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Number: product of primes (Corbettmaths Video 223), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What does it mean to write a number as a product of its prime factors?
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To express the number as a multiplication of prime numbers only (e.g., 12 = 2 × 2 × 3).
What is 24 written as a product of its prime factors in index form?
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2³ × 3
What does index form mean when writing prime factors?
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Using exponents to show repeated prime factors (e.g., 2 × 2 × 2 = 2³).
If a number is written as 2 × 3² × 5, what is the actual number?
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90 (2 × 9 × 5 = 90).
Given that 18000 = 2^a × 3^b × 5^c, the value of a is ?.
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4
What is 48 written as a product of its prime factors in index form?
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2⁴ × 3
How can you find the HCF of two numbers using their prime factorizations?
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Take the lowest power of each common prime factor.
How can you find the LCM of two numbers using their prime factorizations?
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Take the highest power of each prime factor that appears in either number.
If m = 2³ × 5, what is 10m as a product of primes?
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2⁴ × 5² (since 10 = 2 × 5, combine with m's factors).
If y = 3² × 5⁴, what is 50y as a product of prime factors in index form?
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2 × 3² × 5⁵ (since 50 = 2 × 5², add exponents for matching bases).
What is the Highest Common Factor (HCF) of y and 5y?
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y
Given 16200 = 2³ × 3⁴ × 5², what is the lowest whole number by which 16200 needs to be multiplied to make a cube number?
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150 (= 2² × 3² × 5, to make all exponents divisible by 3)
Given 4116 = 2² × 3 × 7³, what is the lowest integer by which 4116 needs to be multiplied to make a square number?
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3 (to make the exponent of 3 even)
For a number to be a perfect square, what must be true about the exponents in its prime factorization?
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All exponents must be even.
For a number to be a perfect cube, what must be true about the exponents in its prime factorization?
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All exponents must be divisible by 3.
If A = 3³ × c and B = 3² × c² × d, and HCF(A,B) = 99, what does this tell us about c?
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c must equal 11, because HCF = 3² × c = 99, so c = 11
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