Write $3150$ as a product of its prime factors. [1] The highest common factor (HCF) of two numbers

Question

Write $3150$ as a product of its prime factors. [1] The highest common factor (HCF) of two numbers is $21$. The lowest common multiple (LCM) of the two numbers is $3150$. Both numbers are greater than $70$. Find the two numbers. [2] Use prime factors to explain why $14\times56$ is a perfect square.[1] $p$ and $q$ are both prime numbers. Find the values of $p$ and $q$ so that $14\times56\div\dfrac pq$ is a perfect cube.[2]

Accepted Answer

(a)(i) $2\times3^2\times5^2\times7$ (a)(ii) $126,525$ (b)(i) $2^4\times7^2$ (b)(ii) $p=2,q=7$

2025 CGS PRELIMS P1 Q18

2025 CGS PRELIMS P1 Q18

Solution:

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