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)
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SOLUTION:--
given by
let , q= 2^a×3^b-----------en(1)
then HCF(72,q) = 12
= HCF( 2^3×3^2 , 2^a×2^b) = 2^2×3
= now ,
72 =2×2×2×3×3
q= 2^a×2^b
___________________________
hcf = 12 = 2×2×3
2×2 = 2^2 = 2^a , 3= 3^1= 3^b
a=2 , b= 1
put value of a,b in eq(1)
q = 2^a×3^b
q = 2^2×3
[ q=12] ans
given by
let , q= 2^a×3^b-----------en(1)
then HCF(72,q) = 12
= HCF( 2^3×3^2 , 2^a×2^b) = 2^2×3
= now ,
72 =2×2×2×3×3
q= 2^a×2^b
___________________________
hcf = 12 = 2×2×3
2×2 = 2^2 = 2^a , 3= 3^1= 3^b
a=2 , b= 1
put value of a,b in eq(1)
q = 2^a×3^b
q = 2^2×3
[ q=12] ans
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