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