The sum of two numbers is 528 and their HCF i | vedclass

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(A) Let the two numbers be $33a$ and $33b$,where $a$ and $b$ are coprime numbers (i.e.,$gcd(a, b) = 1$).Given that the sum of the numbers is $528$,we

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$4$

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(A) Let the two numbers be $33a$ and $33b$,where $a$ and $b$ are coprime numbers (i.e.,$gcd(a, b) = 1$).Given that the sum of the numbers is $528$,we have $33a + 33b = 528$.Dividing by $33$,we get $a + b = \frac{528}{33} = 16$.We need to find pairs $(a, b)$ such that $a + b = 16$ and $gcd(a, b) = 1$ (since $HCF$ is $33$): Possible pairs $(a, b)$ where $a Note: $(2, 14), (4, 12), (6, 10), (8, 8)$ are excluded because they have a common factor other than $1$.Thus,there are $4$ such pairs.

The sum of two numbers is $528$ and their $HCF$ is $33$. The number of pairs of numbers satisfying the above conditions is

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