Question

If HCF (72, q) = 12 then how many values can q
take (assume q be a product of a power of 2 and a
power of 3 only)? ​

Answer 1

Step-by-step explanation:

We have q= 2a 3b

HCF (72 , x) = 12

72 = 23 . 32

HCF (72 , x) = HCF (23 . 32 , 2a 3b) = 22.3

So a is less than 3 ( as if a is 3 or greater than 3 then HCF must contain a factor 23 )

and also a is greater than or equal to 2 ( because HCF 22.3must divided 2a .3bso exponent of 2 must be greater than or equal to 2 )

hence 2<a<3 = a = 2

Now b must be greater than or equal to exponent of 3 in HCF (ie. , 1) and also less than or equal to exponent of 3 in 72 ie ., 2

so we get 1<b<2 = b = 1

so a = 2 and b = 1 . so q can take only one value taht is 22. 3 = 12

please mark me as the brainliest and please follow me and then I will follow you.