AQA · Mathematics · 8300
GCSE Maths: Number: product of primes (squares/cubes)
Number · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Number: product of primes (squares/cubes) (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 is the prime factorization of 24 in index form?
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2³ × 3
What number equals 2 × 3² × 5?
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90
If 3x² = 75 and x is a prime number, what is x?
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x = 5. Dividing both sides by 3 gives x² = 25, so x = 5.
If 3x³ = 375 and x is a prime number, what is x?
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x = 5. Dividing both sides by 3 gives x³ = 125, so x = 5.
If y = 3² × 5⁴, what is 50y as a product of prime factors in index form?
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2 × 5² × 3² × 5⁴ = 2 × 3² × 5⁶
What is the HCF of 48 and 56?
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8. (48 = 2⁴ × 3 and 56 = 2³ × 7; HCF uses minimum powers of common primes: 2³ = 8)
What is the LCM of 60 and 75?
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300. (60 = 2² × 3 × 5 and 75 = 3 × 5²; LCM uses maximum powers: 2² × 3 × 5² = 300)
If C = 2⁵ × 3² × 7⁴ and D = 2 × 3² × 5 × 7², what is the HCF of C and D?
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2 × 3² × 7² = 882. Take the minimum power of each common prime factor.
If C = 2⁵ × 3² × 7⁴ and D = 2 × 3² × 5 × 7², what is the LCM of C and D?
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2⁵ × 3² × 5 × 7⁴. Take the maximum power of each prime factor appearing in either number.
What is the HCF of y and 5y?
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y. The HCF of a number and its multiple is the smaller number itself.
Given 16200 = 2³ × 3⁴ × 5², what is the smallest number by which 16200 must be multiplied to make a cube number?
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2² × 3² × 5 = 180. Each prime power in a cube must be divisible by 3, so multiply by what's needed to make each exponent a multiple of 3.
Given 4116 = 2² × 3 × 7³, what is the smallest integer by which 4116 must be multiplied to make a square number?
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3. Each prime power in a square must be even, so multiply by 3 to make the exponent of 3 equal to 2.
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