Find the hcf and lcm of 306 and 54. verify that hcf × lcm = product of the two numbers.

306=2*153=2*3*51=2*3*3*17
54=2*27=2*3*9=2*3*3*3,
so 306= 2*3*3*17, and 54 = 2*3*3*3
GCF we are looking for all factors that belong to both of these numbers, that are common for both numbers.
 306= 2*3*3*17, 
 54 = 2*3*3*3
GCF = 2*3*3

LCM should include all factors that belong as first as second numbers, and we take prime factor from the number that has maximum repetition of it
306 = 2*3*3*17
54=2*3*3*3
We can see 2 - one time, 3 - 3 times , and 17 - one time
LCM =2*3*3*3*17

Product of two numbers : 306*54=(2*3*3*17) * (2*3*3*3)= 2²*2⁵*17
HCF*LCM=(2*3*3)*(2*3*3*3*17)=2²*3⁵*17
So we can see that
 Product of two numbers = HCF*LCM=2²*3⁵*17

If you need you can calculate
 306= 2*3*3*17, 
 54 = 2*3*3*3
GCF = 2*3*3=18
LCM =2*3*3*3*17=918
GCF*LCM=18*918=16524
Product of 306*54= 16524