**QUESTION:** Find the HCF and LCM of 264 and 110.

264=2\times2\times2\times3\times11 And 110=2\times5\times11 Then, we need to draw a Venn diagram with one circle for prime factors of 264 and another for prime factors of 110. Then, the first step to filling in this diagram is to look for any prime factors that 264 and 110 have in common. For each shared prime factor, we will cross it off both factor lists, and then write it once in the intersection of the two circles. After all shared factors are crossed off, write the rest of the prime factors in their appropriate circles. The result should look something like the diagram below. Then, we find the HCF by multiplying the numbers in the intersection: \text{HCF }=2\times11=22 And find the LCM by multiplying all the numbers in the Venn diagram together: \text{LCM }=2\times2\times2\times3\times5\times11=1,320

ANSWER: Firstly, we need to find the prime factorisations of 264 and 110. Here, we will do this using prime factor trees.

So, we get that

264=2\times2\times2\times3\times11

And

110=2\times5\times11

Then, we need to draw a Venn diagram with one circle for prime factors of 264 and another for prime factors of 110. Then, the first step to filling in this diagram is to look for any prime factors that 264 and 110 have in common. For each shared prime factor, we will cross it off __both factor lists__, and then write it once in the intersection of the two circles.

After all shared factors are crossed off, write the rest of the prime factors in their appropriate circles. The result should look something like the diagram below.

Then, we find the HCF by multiplying the numbers in the intersection:

\text{HCF }=2\times11=22

And find the LCM by multiplying all the numbers in the Venn diagram together:

\text{LCM }=2\times2\times2\times3\times5\times11=1,320