Question
Work out the highest common factor (HCF) of 36 and 90.
▶️Answer/Explanation
To find the highest common factor (HCF) of 36 and 90, we can use the method of prime factorization.
Prime factorize both numbers.
36 can be expressed as\( 2^2\times 3^2.\)
90 can be expressed as \(2\times 3^2\times 5.\)
Identify the common prime factors and their lowest powers.
The common prime factors between 36 and 90 are 2 and 3. The lowest power of 2 is 1, as it appears only once in 90. The lowest power of 3 is 2, as it appears twice in both 36 and 90.
Multiply the common prime factors with their lowest powers.
HCF \(= 2^1\times 3^2 = 2 \times 9 = 18.\)
Therefore, the highest common factor (HCF) of 36 and 90 is 18.
Question
Find the lowest common multiple (LCM) of 36 and 48.
Answer/Explanation
Ans:
144
Question
(a) Write 2016 as the product of prime factors.
(b) Write 2016 in standard form.
Answer/Explanation
Ans:
(a) \(2^5 \times 3^2 \times 7\) oe final answer
(b) \(2.016 \times 10^3\)