Question

If x= ab² and y=a²b where a and b are prime, then HCF(x,y) is *


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Answer 1

Answer:

If x : a3 bcz,y = 762" find HCF (x, y)

Answer 2

Answer:

Required H(x,y) is ab.

Step-by-step explanation:

Here given numbers are $x = a {b}^{2} \: and \: y = {a}^{2} b$

We want to find HCF of these numbers.

HCF means Highest Common Factor.

By one examples we can understand this concept more easily.

We are taking four numbers 20,50,70,100.

By prime factorisation,

$20 = 2 \times 2 \times 5 \\ 50 = 2 \times 5 \times 5 \\ 70 = 2 \times 5 \times 7 \\ 100 = 2 \times 2 \times 5 \times 5$

Here highest common factor of 20,50,70 and 100 is $(2 \times 5) = 10$

So,HCF of 20,50,70 and 100 is 10.

Here numbers are $x = a {b}^{2} \: and \: y = {a}^{2} b$

By prime factorisation,

$x = a {b}^{2} = a \times b \times b \\ y = {a}^{2} b = a \times a \times b$

So, highest common factor of

$x = a {b}^{2} \: and \: y = {a}^{2} b$

is $(a \times b) = ab$

So,HCF of $x = a {b}^{2} \: and \: y = {a}^{2} b$

is ab.

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